Erich Hecke (20 September 1887 – 13 February 1947) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
O ...
known for his work in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathe ...
and the theory of
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...
s.
Biography
Hecke was born in
Buk,
Province of Posen
The Province of Posen (german: Provinz Posen, pl, Prowincja Poznańska) was a province of the Kingdom of Prussia from 1848 to 1920. Posen was established in 1848 following the Greater Poland Uprising as a successor to the Grand Duchy of Posen, w ...
,
German Empire
The German Empire (), Herbert Tuttle wrote in September 1881 that the term "Reich" does not literally connote an empire as has been commonly assumed by English-speaking people. The term literally denotes an empire – particularly a hereditar ...
(now
Poznań
Poznań () is a city on the River Warta in west-central Poland, within the Greater Poland region. The city is an important cultural and business centre, and one of Poland's most populous regions with many regional customs such as Saint John ...
,
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
). He obtained his doctorate in
Göttingen
Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911.
General information
The or ...
under the supervision of
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
.
Kurt Reidemeister
Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
Life
He was a brother of Marie Neurath.
Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götting ...
and
Heinrich Behnke
Heinrich Adolph Louis Behnke ( Horn, 9 October 1898 – Münster, 10 October 1979) was a German mathematician and rector at the University of Münster.
Life and career
He was born into a Lutheran family in Horn, a suburb of Hamburg. He a ...
were among his students.
In 1933 Hecke signed the ''
Loyalty Oath of German Professors to Adolf Hitler and the National Socialist State''.
Hecke died in
Copenhagen,
Denmark
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, established ...
.
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. Th ...
, in the foreword to his text Basic Number Theory
says: "To improve upon Hecke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task", referring to Hecke's book "Lectures on the Theory of Algebraic Numbers."
Research
His early work included establishing the
functional equation
In mathematics, a functional equation
is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning ...
for the
Dedekind zeta function
In mathematics, the Dedekind zeta function of an algebraic number field ''K'', generally denoted ζ''K''(''s''), is a generalization of the Riemann zeta function (which is obtained in the case where ''K'' is the field of rational numbers Q). It c ...
, with a proof based on
theta function
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field the ...
s. The method extended to the
L-function
In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give ri ...
s associated to a class of characters now known as
Hecke character In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of
''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and ce ...
s or
idele class character In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of
''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and ce ...
s; such L-functions are now known as Hecke L-functions. He devoted most of his research to the theory of
modular form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...
s, creating the general theory of
cusp form In number theory, a branch of mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion.
Introduction
A cusp form is distinguished in the case of modular forms for the modular g ...
s (
holomorphic
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivati ...
, for GL(2)), as it is now understood in the classical setting.
Recognition
He was a Plenary Speaker of the
ICM in 1936 in Oslo.
See also
*
List of things named after Erich Hecke
*
Hecke algebra (disambiguation) In mathematics, a Hecke algebra
In mathematics, the Hecke algebra is the algebra generated by Hecke operators.
Properties
The algebra is a commutative ring.
In the classical elliptic modular form theory, the Hecke operators ''T'n'' with ''n'' ...
*
Tate's thesis
In number theory, Tate's thesis is the 1950 PhD thesis of completed under the supervision of Emil Artin at Princeton University. In it, Tate used a translation invariant integration on the locally compact group of ideles to lift the zeta functi ...
References
External links
*
*
1887 births
1947 deaths
People from Poznań County
People from the Province of Posen
20th-century German mathematicians
Number theorists
University of Hamburg faculty
University of Basel faculty
University of Göttingen faculty
University of Breslau alumni
University of Göttingen alumni
{{Germany-academic-bio-stub