Kurt Mahler | Academic Influence

Kurt Mahler's AcademicInfluence.com Rankings

Kurt Mahler

Mathematics

#804

Historical Rank

Number Theory

#33

Historical Rank

Measure Theory

#293

Historical Rank

mathematics Degrees

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Mathematics

Kurt Mahler's Degrees

PhD Mathematics University of Göttingen

Why Is Kurt Mahler Influential?

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According to Wikipedia, Kurt Mahler FRS was a German mathematician who worked in the fields of transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Career Mahler was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D. from Johann Wolfgang Goethe University of Frankfurt am Main in 1927; his advisor was Carl Ludwig Siegel. He left Germany with the rise of Adolf Hitler and accepted an invitation by Louis Mordell to go to Manchester. However, at the start of World War II he was interned as an enemy alien in Central Camp in Douglas, Isle of Man, where he met Kurt Hirsch, although he was released after only three months. He became a British citizen in 1946.

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Kurt Mahler's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

An inequality for the discriminant of a polynomial. (1964) (215)
An application of Jensen's formula to polynomials (1960) (200)
Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen (1929) (191)
Ein Übertragungsprinzip für konvexe Körper (1939) (182)
On Some Inequalities for Polynomials in Several Variables (1962) (162)
On a Special Functional Equation (1940) (161)
An Interpolation Series for Continuous Functions of a p-adic Variable. (1958) (159)
p-adic numbers and their functions (1981) (154)
Zur Approximation der Exponentialfunktion und des Logarithmus. Teil I. (1932) (144)
Zur Approximation algebraischer Zahlen. I (1933) (134)
Zur Approximation der Exponentialfunktion und des Logarithmus. Teil II. (110)
On the representation of integers by binary forms (1961) (107)
An unsolved problem on the powers of 3/2 (1968) (106)
An Analogue to Minkowski's Geometry of Numbers in a Field of Series (1941) (93)
Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen (1930) (92)
Über das Maß der Menge allerS-Zahlen (1932) (83)
On lattice points in n-dimensional star bodies I. Existence theorems (1946) (82)
Introduction to P-Adic Numbers and their Functions (1973) (79)
On a Theorem of Liouville in Fields of Positive Characteristic (1949) (76)
Uber das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen (1930) (76)
The Spectrum of an Array and its Application to the Study of the Translation Properties of a Simple Class of Arithmetical Functions: Part Two On the Translation Properties of a Simple Class of Arithmetical Functions (1927) (74)
On a special function (1980) (72)
Lectures on Transcendental Numbers (1976) (72)
Some suggestions for further research (1984) (66)
On the fractional parts of the powers of a rational number (II) (1957) (61)
An introduction to Diophantine Approximation. By J. W. S. Cassbls. Cambridge tracts in mathematics and mathematical physics, No. 45. Pp. 166. 22s. 6d. 1957. (Cambridge) (1959) (58)
On the approximation of logarithms of algebraic numbers (1953) (57)
On the zeros of the derivative of a polynomial (1961) (53)
On algebraic differential equations satisfied by automorphic functions (1969) (51)
On the Taylor coefficients of rational functions (1956) (48)
On the Densest Packing of Circles (1944) (41)
On a class of non-linear functional equations connected with modular functions (1976) (39)
Zur Approximation algebraischer Zahlen. III. (1933) (39)
On the Number of Integers Which Can Be Represented By a Binary Form (1938) (38)
Arithmetic properties of lacunary power series with integral coefficients (1965) (36)
Über transzendente $P$-adische Zahlen (1935) (36)
On a Geometrical Representation of p-Adic Numbers (1940) (36)
Über einen Satz von Mellin (1928) (35)
Remarks on a paper by W. Schwarz (1969) (35)
Applications of some formulae by hermite to the approximation of exponentials and logarithms (1967) (34)
Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen (34)
On the Approximation of π (1953) (33)
Ein Beweis des Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen (1931) (31)
On the Lattice-Points on Curves of Genus (1935) (30)
On Exceptional Points on Cubic Curves (1940) (30)
On the fractional parts of the powers of a rational number (1939) (29)
Inequalities for ideal bases in algebraic number fields (1964) (29)
On Compound Convex Bodies (II) (1955) (28)
On two extremum properties of polynomials (1963) (27)
On some irrational decimal fractions (1981) (25)
On a paper by A. Baker on the approximation of rational powers of e (1975) (25)
G-adic Numbers and Roth's Theorem (1961) (23)
A generalization of Farey sequences: Some exploration via the computer (1971) (20)
On the coefficients of transformation polynomials for the modular function (1974) (19)
The theorem of Minkowski-Hlawka (1946) (17)
Polar analogues of two theorems by Minkowski (1974) (17)
A theorem on diophantine approximations (1976) (17)
Farey section in k(i) and k(ρ) (1951) (17)
Ein Beweis der Transzendenz der P-adischen Exponentialfunktion. (1933) (16)
On the transcendency of the solutions of a special class of functional equations (1975) (15)
Applications of a theorem by A. B. Shidlovski (1968) (15)
Fifty years as a mathematician (1982) (15)
On the order function of a transcendental number (1971) (14)
Zur Approximation algebraischer Zahlen. II (1933) (14)
ON MINKOWSKI'S THEORY OF REDUCTION OF POSITIVE DEFINITE QUADRATIC FORMS (1938) (14)
On the Chinese Remainder Theorem (1958) (13)
On a class of entire functions (1967) (13)
Some arithmetical properties of the convergents of a continued fraction (1939) (13)
Lattice Points in Two-Dimensional Star Domains (II) (1946) (12)
Note on Hypothesis K of Hardy and Littlewood (1936) (11)
On the coefficients of the $2^n$-th transformation polynomial for j(ω) (1972) (11)
On the approximation of algebraic numbers by algebraic integers (1963) (10)
Arithmetical properties of the digits of the multiples of an irrational number (1973) (10)
ON LATTICE POINTS IN A CYLINDER (1946) (10)
On Thue's theorem. (1984) (10)
On the approximation of real numbers by roots of integers (1967) (10)
Über die Annäherung algebraischer Zahlen durch periodischen Algorithmen (1937) (9)
Apparatur zum kontinuierlichen Aufzeichnen von Sorptionsisothermen (1961) (9)
Über Pseudobewertungen. I (1936) (8)
A correction to the paper An Interpolation Series for continuous functions of a p-adic variable. (1961) (8)
On the Generating Function of the Integers with a Missing Digit (1951) (8)
On a class of transcendental decimal fractions (1976) (8)
On a theorem in the geometry of numbers in a space of Laurent series (1983) (8)
Integers with Digits 0 or 1 (1986) (7)
On The Critical Lattices of Arbitrary Point Sets (1949) (7)
Minkowski's fundamental inequality for reduced positive quadratic forms (1978) (7)
On a special nonlinear functional equation (1981) (7)
On the continued fractions of quadratic and cubic irrationals (1949) (7)
On lattice points in a convex decagon (1949) (7)
Zur Fortsetzbarkeit gewisser Dirichletscher Reihen (1930) (7)
Über die Annäherung algebraischer Zahlen durch periodische Algorithmen (1937) (7)
A Problem of Diophantine Approximation in Quaternions (1945) (6)
On Reduced Positive Definite Ternary Quadratic Forms (1940) (6)
Ueber die nullstellen der unvollstaendigen Gammafunktionen (1930) (6)
A remark on Siegel's theorem on algebraic curves (1955) (5)
On Lattice Points in An Infinite Star Domain (1943) (5)
On a Property of Positive Definite Ternary Quadratic Forms (1940) (5)
A theorem of B. Segre (1945) (5)
On the Taylor coefficients of rational functions (1957) (5)
Equations in free metabelian groups. (1965) (5)
A remark on a paper of mine on polynomials (1964) (5)
An inequality for a pair of polynomials that are relatively prime (1964) (5)
An addition to a note of mine (1976) (5)
On the zeros of a special sequence of polynomials (1982) (5)
On rational approximations of the exponential function at rational points (1974) (5)
On lattice points in the domain |xy | ≤1, | x + y | ≤√5, and applications to asymptotic formulae in lattice point theory (II) (1944) (4)
Über Pseudobewertungen. III (1936) (4)
Über Konvergenzfragen bei Polynomialinterpolation mit äquidistanten Knoten. I. (1961) (4)
On a Theorem of Minkowski on Lattice Points in Non-Convex Point Sets (1944) (4)
A lecture on the geometry of numbers of convex bodies (1971) (4)
On the Product of Two Complex Linear Polynomials in Two Variables (1940) (3)
Über Beziehungen zwischen der Zahle und Liouvilleschen Zahlen (1930) (3)
Note on Lattice Points in Star Domains (1942) (3)
On a problem in Diophantine approximations (1955) (3)
An arithmetic property of groups of linear transformations (1959) (3)
Über Pseudobewertungen. II (1936) (3)
Über die konvexen Körper, die sich einem Sternkörper einbeschreiben lassen (1956) (3)
Vollautomatische Aufzeichnung der Austauschgeschwindigkeit über der Konzentration beim Trocknen (1959) (3)
On Hecke's Theorem on the Real Zeros of the L‐Functions and the Class Number of Quadratic Fields (1934) (3)
On the successive minima of a bounded star domain (1948) (3)
Über die Nullstellen der Abschnitte der hypergeometrischen Reihe (1929) (2)
A necessary and sufficient condition for transcendency (1975) (2)
An elementary existence theorem for entire functions (1971) (2)
On the analytic solution of certain functional and difference equations (1983) (2)
On two analytic functions (1987) (2)
An arithmetic remark on entire periodic functions (1971) (2)
On a class of diophantine inequalities (1973) (2)
A p-adic analogue to a theorem by J. Popken (1973) (2)
A Factorial Series for the Rational Multiples of e (1958) (2)
On the digits of the multiples of an irrational p-adic number (1974) (2)
XVII.—Invariant Matrices and the Geometry of Numbers (1957) (2)
On certain non-archimedean functions analogous to complex analytic functions (1976) (2)
On a theorem by E. Bombieri (1960) (2)
The successive minima in the geometry of numbers and the distinction between algebraic and transcendental numbers (1986) (2)
A matrix representation of the primitive residue classes (mod $2n$) (1957) (2)
On the minima of compound quadratic forms (1955) (1)
ON THE DIVISION-VALUES OF WEIERSTRASS'S ℘-FUNCTION (1935) (1)
On two definitions of the integral of a p-adic function (1980) (1)
A property of the star domain |xy| ≤ 1 (1956) (1)
Abelian Modular Functions (1953) (1)
On a theorem of Shidlovski (1959) (1)
On a Special Class of Diophantine Equations: II (1938) (1)
How I Became a Mathematician (1974) (1)
On the transcendency of the solutions of a special class of functional equations: Corrigendum (1976) (1)
On the Lattice Determinants of Two Particular Point Sets (1953) (1)
Walzen‐Schachttrockner zum Trocknen von pastenförmigen und breiigen Produkten, besonders von Farbstoffen (1965) (1)
Remarks on Ternary Diophantine Equations (1942) (1)
The representation of squares to the base 3 (1989) (1)
On the Minimum of Positive Definite Hermitian Forms (1939) (1)
Über einen Satz von Th. Schneider (1939) (1)
International transfers (1976) (1)
Appendix A: Another Proof of a Lemma by Schneider (1961) (0)
Formal power series as solutions of algebraic differential equations (1976) (0)
Appendix C: The Approximation Theorems over Algebraic Number Fields (1961) (0)
Chapter I: Valuations and Pseudo-valuations (1961) (0)
The p‐th Compound of a Sphere (1955) (0)
Bestimmung der Restfeuchte über Gleichgewichtsdampfdruck und Sorptionsisotherme (1964) (0)
Linear differential equations: Shidlovski's theorems on the transcendency and algebraic independence of values of siegel E-functions (1976) (0)
Chapter VI: The Approximation Polynomial (1961) (0)
Allgemeine Theorie der algebraischen Zahlen. By Ph. Furtwangler, H. Hasse and W. Jehne. Enzyklopädie der mathematischen Wissenschaften. Band I/2. Teil: C. Reine Zahlentheorie. Heft 8, II, Artikel 19. Pp. 50. 1953. (Teubner, Leipzig) (1956) (0)
Chapter II: The p-adic, g-adic, and g*-adic Series (1961) (0)
Chapter V: Roth's Lemma (1961) (0)
Correction to the paper: On a theorem by E. Bombieri (1961) (0)
Thomas Ranken Lyle Medal 1977 (1975) (0)
Ok the Number of Integer8 Which Can Be Rcepr'esented by a Binary For,m (0)
Index of Democratic Values 1994 (1995) (0)
Problems for Solution: 5101-5110 (1963) (0)
The write stuff. (1989) (0)
Society's notes (1948) (0)
Appendix B: A Theorem by M. Cugiani (1961) (0)
Linear differental equations: The lemmas of Shidlovski (1976) (0)
Chapter VIII: The Second Approximation Theorem (1961) (0)
A Problem in Elementary Geometry (1954) (0)
The harvest of life. (1989) (0)
Convergent laurent series and formal laurent series (1976) (0)
Chapter III: A Test for Algebraic or Transcendental Numbers (1961) (0)
First results on the values of analytic functions at algebraic points (1976) (0)
Problems for Solution: 4788-4792 (1958) (0)
Part 1: p-adic and g-adic Numbers, and Their Approximations (1961) (0)
Linear differential equations: A lower bound for the rank of the values of finitely many siegel E-functions at algebraic points (1976) (0)
A new transfer principle in the geometry of numbers (1986) (0)
Advanced Problems: 5253-5260 (1965) (0)
L. J. Mordell (1972) (0)
Title and Copyright Pages (1961) (0)
Part 2: Rational Approximations of Algebraic Numbers. The Problem and Its History (1961) (0)
Existence and first properties of transcendental numbers (1976) (0)
Applications of Shidlovski's main theorems to special functions (1976) (0)
Problems for Solution: 4816-4821 (1958) (0)
Chapter VII: The First Approximation Theorem (1961) (0)

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