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Theorem in p-adic analysis
In mathematics, Mahler's theorem, introduced by Kurt Mahler (1958), expresses any continuous p-adic function as an infinite series of certain special
Mahler's_theorem
Characterizes sets of lattices that are bounded in a certain sense
In mathematics, Mahler's compactness theorem, proved by Kurt Mahler (1946), is a foundational result on lattices in Euclidean space, characterising sets
Mahler's_compactness_theorem
Branch of number theory
usual real absolute value or a p-adic absolute value. Mahler's theorem, introduced by Kurt Mahler, expresses continuous p-adic functions in terms of polynomials
P-adic_analysis
The zeros of a linear recurrence relation mostly form a regularly repeating pattern
In algebraic number theory, the Skolem–Mahler–Lech theorem states that if a sequence of numbers satisfies a linear recurrence with constant coefficients
Skolem–Mahler–Lech_theorem
German mathematician (1903–1988)
Mahler spoke Chinese and was an expert photographer. Mahler's inequality Mahler measure Mahler polynomial Mahler volume Mahler's theorem Mahler's compactness
Kurt_Mahler
Uniqueness theorem in complex analysis
In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it
Carlson's_theorem
Topics referred to by the same term
Mahler, a mountain in Colorado Search for "Mahler" on Wikipedia. Maher (disambiguation) Mahler measure Mahler's compactness theorem Mahler's theorem Maler
Mahler_(disambiguation)
numbers Minkowski's theorem Pick's theorem Mahler's compactness theorem Mahler measure Effective results in number theory Mahler's theorem Brun sieve Function
List_of_number_theory_topics
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Branch of discrete mathematics
none contains any other? The latter question is answered by Sperner's theorem, which gave rise to much of extremal set theory. The types of questions
Combinatorics
Theorem about Diophantine approximations
Kronecker's theorem is a theorem about diophantine approximation, introduced by Leopold Kronecker (1884). Kronecker's approximation theorem had been firstly
Kronecker's_theorem
Number of subsets of a given size
coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥
Binomial_coefficient
representation of an integer Mahler's theorem Multinomial distribution Multinomial coefficient, Multinomial formula, Multinomial theorem Multiplicities of entries
List of factorial and binomial topics
List_of_factorial_and_binomial_topics
Measure of polynomial height
range of Mahler's measure". Canadian Mathematical Bulletin. 24 (4): 453–469. doi:10.4153/cmb-1981-069-5. Boyd, David (1981b). "Kronecker's Theorem and Lehmer's
Mahler_measure
Number system extending the rational numbers
convexity and the Hahn–Banach theorem are different. Two important concepts from p-adic analysis are Mahler's theorem, which characterizes every continuous
P-adic_number
Prasanta Chandra Mahalanobis (প্রশান্ত চন্দ্র মহলানবিস) Mahler measure, Mahler's theorem – Kurt Mahler Maillard reaction Malmquist bias, effect – Karl Gunnar
Scientific phenomena named after people
Scientific_phenomena_named_after_people
On the transcendence of a large class of numbers
In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers. It was originally proved independently in 1934
Gelfond–Schneider_theorem
Discrete analog of a derivative
)=\Delta 0\cdot P\left(\xi \right).} In analysis with p-adic numbers, Mahler's theorem states that the assumption that f is a polynomial function can be weakened
Finite_difference
Gives conditions for a space of compact Riemann surfaces of genus > 1 to be compact
consequence of a theorem about the compactness of sets of discrete subgroups of semisimple Lie groups generalizing Mahler's compactness theorem. Mumford, David
Mumford's_compactness_theorem
German mathematician (1927–2023)
Springer-Verlag 1984. Robinson, A.; Roquette, P. On the finiteness theorem of Siegel and Mahler concerning Diophantine equations. J. Number Theory 7 (1975),
Peter_Roquette
Function that quantifies how near a number is to being rational
(see Khinchin's theorem) 0 < | x − p q | < 1 q 2 ln q {\displaystyle 0<\left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{2}\ln q}}} Kurt Mahler extended the
Irrationality_measure
French mathematician (1936–1993)
arithmetic of local fields. Her procedure (now known as Amice theorem) generalized Mahler's theorem. In 1965, she gave one of the Peccot Lectures (for distinguished
Yvette_Amice
Result in field theory about zeros of formal power series
field of p-adic complex numbers. Strassman's theorem may also be used to prove the Skolem-Mahler-Lech theorem, which states that the set of indices at which
Strassmann's_theorem
Unsolved problem in mathematics
proving the Skolem–Mahler–Lech theorem on the zeros of a sequence satisfying a linear recurrence with constant coefficients. This theorem states that, if
Skolem_problem
In mathematics, a non-algebraic number
551–560. doi:10.1155/S0161171295000706. Mahler, Kurt; Mordell, Louis Joel (1968-06-04). "Applications of a theorem by A. B. Shidlovski". Proceedings of the
Transcendental_number
Northern Irish physicist (1928–1990)
physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022
John_Stewart_Bell
Mathematical problem in number theory
whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909. Waring's problem has its own Mathematics
Waring's_problem
Subset of a topological space whose closure is compact
integrability, and the concept of normal family in complex analysis. Mahler's compactness theorem in the geometry of numbers characterizes relatively compact subsets
Relatively_compact_subspace
Study of numbers that are not solutions of polynomials with rational coefficients
coefficients), in both qualitative and quantitative ways. The fundamental theorem of algebra tells us that if we have a non-constant polynomial with rational
Transcendental_number_theory
German mathematician (1896–1981)
known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method, Siegel's lemma and the Siegel
Carl_Ludwig_Siegel
Branch of mathematics
Ronen Eldan in a 2013 paper. Symmetrization. Dvoretzky's theorem (or the Dvoretzky–Milman theorem) states that every centrally symmetric convex body in a
Asymptotic_geometry
Type of algebraic number
number. Perron numbers are named after Oskar Perron; the Perron–Frobenius theorem asserts that, for a real square matrix with positive algebraic entries
Perron_number
Proposed lower bound on the Mahler measure for polynomials with integer coefficients
Lehmer's conjecture, also known as the Lehmer's Mahler measure problem, is a problem in number theory raised by Derrick Henry Lehmer. The conjecture asserts
Lehmer's_conjecture
Class of irrational numbers
usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem. Lemma: If α {\displaystyle
Liouville_number
American-born British mathematician (1888-1972)
Stickelberger's theorem?" The speaker said "No it isn't." A few minutes later the person interrupted again and said "I'm positive that's Stickelberger's theorem!" The
Louis_J._Mordell
Mathematical functions that quantify complexity
height functions can be used to prove asymptotic results such as Baker's theorem in transcendental number theory which was proved by Alan Baker (1966, 1967a
Height_function
Polynomial whose coefficients are all 1 or −1
structured subclass with explicitly computable norms. The 2020 flatness theorem settles the existence of uniformly bounded upper and lower constants, but
Littlewood_polynomial
Mathematics analytic function
algebraically transcendental are transcendentally transcendental. Hölder's theorem shows that the gamma function is in this category. Hypertranscendental
Hypertranscendental_function
Mathematical constant; sum of 1 / 2^2^n
(December 1991), pp. 947–949, doi:10.2307/2324154, JSTOR 2324154. Theorem 1.1.2, Mahler Functions and Transcendence, Kumiko Nishioka, Berlin, Heidelberg:
Kempner_number
2021) Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
inequality Maclaurin's inequality Mahler's inequality Muirhead's inequality Newton's inequalities Stein–Strömberg theorem Binomial coefficient bounds Factorial
List_of_inequalities
Norwegian mathematician
normal form Skolem's paradox Skolem problem Skolem sequence Skolem–Mahler–Lech theorem Skolem, Thoralf (1934). "Über die Nicht-charakterisierbarkeit der
Thoralf_Skolem
American mathematician
of each mathematical research paper in the language of an interactive theorem prover. The goal of this project is to benefit from the increased precision
Thomas_Callister_Hales
Geometry of the location of polynomial roots
For simple roots, this results immediately from the implicit function theorem. This is true also for multiple roots, but some care is needed for the
Geometrical properties of polynomial roots
Geometrical_properties_of_polynomial_roots
stronger conjectures, is at the top of a hierarchy of conjectures and theorems concerning the arithmetic nature of a certain number of values of the exponential
Four_exponentials_conjecture
English mathematician (1939–2018)
National Academy of Sciences, India. Baker generalised the Gelfond–Schneider theorem, which itself is a solution to Hilbert's seventh problem. Specifically
Alan_Baker_(mathematician)
Soviet-Belarusian mathematician (1936–1987)
диофантовых приближениях алгебраическими числами ограниченной степени" (Metric Theorems of Diophantine Approximations and Approximations by Algebraic Numbers of
Vladimir Gennadievich Sprindzuk
Vladimir_Gennadievich_Sprindzuk
Maths conjecture
MR 2471868, S2CID 8483579/ Bárány, Imre; Lovász, László (1982), "Borsuk's theorem and the number of facets of centrally symmetric polytopes", Acta Mathematica
Kalai's_3^d_conjecture
Italian mathematician
Zannier gave a new proof of Siegel's theorem on integral points in 2002 by using a new method based on the subspace theorem. Corvaja was inducted into the Istituto
Pietro_Corvaja
Periodic set of points
cryptography Lattice graph Lattice (module) Lattice (order) Mahler's compactness theorem Reciprocal lattice Unimodular lattice Gruber, Peter M.; Lekkerkerker
Lattice_(group)
French mathematician (1910–1990)
analytic methods. He introduced the Chabauty topology to generalise Mahler's compactness theorem from Euclidean lattices to more general discrete subgroups. His
Claude_Chabauty
Foundational principle in quantum physics
Hardy's Theorem while the version by Bonami–Demange–Jaming covers the full strength of Hardy's Theorem. A different proof of Beurling's theorem based on
Uncertainty_principle
Belgian mathematician (1954–2018)
high-dimensional convex geometry. In 1985, he proved Bourgain's embedding theorem in metric dimension reduction, which states that every metric space can
Jean_Bourgain
Thought experiment of 1867
relations such as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control
Maxwell's_demon
British mathematician (born 1963)
99–132. with Klaus Schmidt: Mixing automorphisms of compact groups and a theorem of Schlickewei, Invent. Math. 111 (1993), no. 1, 69–76. with Qing Zhang:
Thomas_Ward_(mathematician)
Italian mathematician (born 1957)
2002 gave a new proof of Siegel's theorem on integral points by using a new method based upon the subspace theorem. Zannier was an Invited Speaker at
Umberto_Zannier
Brothers Grimm (2005), The Imaginarium of Doctor Parnassus (2009), The Zero Theorem (2013) John Gilling Sid James Escape by Night (1953), Interpol (1957),
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Interpretation of quantum mechanics
between the probability density and the wave function has the status of a theorem, a result of a separate postulate, the "quantum equilibrium hypothesis"
De_Broglie–Bohm_theory
Two-dimensional shape
ISBN 978-3-031-21799-9. MR 4628019. Fejes Tóth, László (1950). "Some packing and covering theorems". Acta Universitatis Szegediensis. 12: 62–67. MR 0038086. Kallus, Yoav
Smoothed_octagon
Theorem in probability theory
Blitzstein and Jessica Hwang, Introduction to Probability, Final Review Notes. Mahler, Howard C.; Dean, Curtis G. (2001). "Chapter 8: Credibility" (PDF). In Casualty
Law_of_total_variance
Austrian composer
Gustav Mahler, conducting. In his later years, he developed an interest in mathematics and mistakenly believed that he had solved Fermat's Last Theorem. This
Josef_Forster_(composer)
German mathematician (born 1958)
curves. A classical result motivating this study is the Narasimhan–Seshadri theorem, a cornerstone of the Simpson correspondence. It asserts that a vector
Christopher_Deninger
American mathematician
with his paper "Regularity theorems and Gersgorin theorems for matrices over rings with valuation". He writes, "Theorems can be extended to non-commutative
Joel_Lee_Brenner
Spanish mathematician
classical study. The usual topics are covered such as (4) Fundamental theorem of projective geometry, (11) projective plane, (12) cross-ratio, (13) harmonic
Luis_Santaló
American mathematician (1905–1991)
The Lehmers also assisted Harry Vandiver with his work on Fermat's Last Theorem, using the Standards Western Automatic Computer to do many calculations
D._H._Lehmer
Nearest integers from a number
less than or equal to x. It is a straightforward deduction from Wilson's theorem that π ( n ) = ∑ j = 2 n ⌊ ( j − 1 ) ! + 1 j − ⌊ ( j − 1 ) ! j ⌋ ⌋ . {\displaystyle
Floor_and_ceiling_functions
Austrian mathematician (1885–1962)
vol. 3 ISBN 3889082033 Several theorems and mathematical concepts are named for Blaschke: Blaschke selection theorem – Sequences of convex sets in a
Wilhelm_Blaschke
(PDF) on 2016-04-19. Retrieved 2015-02-28. Robin Whitty. Lieb's Square Ice Theorem (PDF). Ivan Niven. Averages of exponents in factoring integers (PDF). Steven
List of mathematical constants
List_of_mathematical_constants
Dutch-Australian number theorist
writings, among them a paper on Apéry's theorem on the irrationality of ζ(3) and his book on Fermat's Last Theorem. Van der Poorten received the Australian
Alfred_van_der_Poorten
Bound on the coefficients of a factor polynomial
\ \ \ \|f\|_{1}=\sum \limits _{i=0}^{n}|f_{i}|.} By the fundamental theorem of algebra f {\displaystyle f} has n {\displaystyle n} roots z 1 , z 2
Landau–Mignotte_bound
Infinite sequence of numbers satisfying a linear equation
addition, term-wise multiplication, and Cauchy product. The Skolem–Mahler–Lech theorem states that the zeros of a constant-recursive sequence have a regularly
Constant-recursive_sequence
irrationality of ζ(2) and ζ(3). Later that year he showed that Müntz's theorem holds on every compact subset of the positive real axis of the Lebesgue
Tamás_Erdélyi_(mathematician)
Macbeath regions Mahler volume - a dimensionless quantity that is associated with a centrally symmetric convex body Minkowski's theorem - any convex set
List_of_convexity_topics
Transcendental number(s) with all positive integers in order
C_{10}} is normal in base 10, while Nakai and Shiokawa proved a more general theorem, a corollary of which is that C b {\displaystyle C_{b}} is normal in base
Champernowne_constant
Difference between logarithm and harmonic series
239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285. Mahler, Kurt (4 June 1968). "Applications of a theorem by A. B. Shidlovski" (PDF). Proceedings of the Royal
Euler's_constant
Israeli mathematician and professor
of mathematician Zvi Artstein, best known for his proof of Artstein's theorem. She graduated summa cum laude from Tel Aviv University in 2000, with a
Shiri_Artstein
Sequence of digital values used for synchronisation
} In 2014, Jürgen Willms exhibited counterexamples to an intermediate theorem used in their published proof, showing that the proof as written was incomplete
Barker_code
Academic faculty in north-west England
result for which he is best known, namely the finite basis theorem (or Mordell–Weil theorem), which proved a conjecture of Henri Poincaré. Mordell then
Department of Mathematics, University of Manchester
Department_of_Mathematics,_University_of_Manchester
Sequence of polynomials
Brendt, Bruce C. "RAMANUJAN REACHES HIS HAND FROM HIS GRAVE TO SNATCH YOUR THEOREMS FROM YOU" (PDF). Retrieved 23 November 2013. Weisstein, Eric W. "Bell Polynomial"
Touchard_polynomials
Mathematical relation defining a sequence
sequence Linear differential equation Recurrence relation Skolem–Mahler–Lech theorem Skolem problem Chiang, Alpha (1984). Fundamental Methods of Mathematical
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
Peter Lax, 99, Hungarian-born American mathematician (Lax equivalence theorem, Lax–Friedrichs method), Abel Prize laureate (2005), cardiac amyloidosis
Deaths_in_May_2025
Lowest possible energy of a quantum system or field
Callen and Theodore Welton proved the quantum fluctuation-dissipation theorem (FDT) which was originally formulated in classical form by Nyquist (1928)
Zero-point_energy
Open conjecture in multiplicative Diophantine approximation
invariant under determinant-one diagonal transformations. By Mahler's compactness theorem, failure of Littlewood's conjecture corresponds to relative compactness
Littlewood_conjecture
Swedish mathematician
Pythagorean theorem based on the Pythagorean tiling is sometimes called "Olof Hanner's Jigsaw Puzzle". Hanner, Olof (1951), "Some theorems on absolute
Olof_Hanner
in Pyrrhonian skepticism) Pythagorean – Pythagoras (as in Pythagorean theorem) Pythonic – Monty Python, a more correct eponym, used by Terry Jones, for
List of eponymous adjectives in English
List_of_eponymous_adjectives_in_English
Problem in number theory
0 as a sum of three cubes would give a counterexample to Fermat's Last Theorem for the exponent three, as one of the three cubes would have the opposite
Sums_of_three_cubes
Number, sum of distinct powers of 4
S2CID 122848891. See in particular the discussion following Theorem 4.2. Lehmer, D. H.; Mahler, K.; van der Poorten, A. J. (1986), "Integers with digits
Moser–de_Bruijn_sequence
Malgrange, 95, French mathematician (Malgrange–Ehrenpreis theorem, Malgrange preparation theorem), member of the French Academy of Sciences. Jack Masters
Deaths_in_January_2024
the Equilibrium of Planes; On Floating Bodies; The Method of Mechanical Theorems; On Spiral Lines; On the Sphere and the Cylinder; On the Measurement of
List of most expensive books and manuscripts
List_of_most_expensive_books_and_manuscripts
important for his work in pure mathematics, having authored a number of theorems. Frank Wilczek (born 1951): American theoretical physicist. Along with
List_of_agnostics
Device converting heat flow into usable work at the nanoscale
proposed two formulations of the third law of thermodynamics. The Nernst heat theorem states that a pure substance's entropy approaches zero as temperature nears
Quantum_heat_engine
symbols pave the entrance, and one interior canopy displays the geometrical theorem known to some of us as Pascal's Mystic Hexagram." The mathematical symbols
List of works by Rafael Viñoly
List_of_works_by_Rafael_Viñoly
Triangle inequality in Lp spaces
Mathematical concept Stein 1970, §A.1. Hardy, Littlewood & Pólya 1988, Theorem 202. Bahouri, Chemin & Danchin 2011, p. 4. Mulholland, H. P. (1949). "On
Minkowski_inequality
generalised a theorem due to Wilhelm Magnus, and worked on the structure of tensor spaces. In 1953 he published a joint paper with Kurt Mahler on pseudo-valuations
Paul_Cohn
von Lindemann Proved that π is transcendental (the Lindemann–Weierstrass theorem) 1897 The U.S. state of Indiana Came close to legislating the value 3.2
Chronology of computation of pi
Chronology_of_computation_of_pi
Mathematical invariance under transformations
the case to say that physics is the study of symmetry." See Noether's theorem (which, in greatly simplified form, states that for every continuous mathematical
Symmetry
Nothing Bad Can Happen Our Heroes Died Tonight Patrick She Wolf The Zero Theorem U.S. premieres Afflicted Almost Human Blue Ruin Borgman Commando: A One
List of Fantastic Fest editions
List_of_Fantastic_Fest_editions
matrices Marjorie Batchelor, American mathematician known for Batchelor's theorem on supermanifolds Grace Bates (1914–1996), one of few women in the United
List_of_women_in_mathematics
Modular function in mathematics
Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7. Theorem 4.8 Chudnovsky, David V.; Chudnovsky, Gregory V. (1989), "The Computation
J-invariant
British mathematician (1923–2010)
over 600 articles in these areas, some jointly with colleagues. Hilton's theorem (1955) is on the homotopy groups of a wedge of spheres. It addresses an
Peter_Hilton
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