Erich Hecke

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Erich Hecke

Erich Hecke (born September 20, 1887 in Buk ( Posen Province ), † February 13, 1947 in Copenhagen ) was a German mathematician who mainly worked in the fields of algebraic number theory and the theory of modular forms .

Life

Hecke studied mathematics and natural sciences first at the Universities of Breslau , later in Berlin and Göttingen with Edmund Landau and David Hilbert . In 1910 he received his doctorate under David Hilbert with a thesis on Hilbert's modular functions in two variables, one of Hilbert's problems, namely to search for functions that play the same role in the theory of algebraic number fields and their extensions as the exponential function in the field of circular division or the elliptical module function in imaginary square number fields ("Kronecker's youth dream"). In 1912 he completed his habilitation in Göttingen. In 1915 he received a professorship in Basel , then moved to Göttingen in 1918 and finally to Hamburg in 1919 . From 1929 until his death he was co-editor of the prestigious Mathematische Annalen . Hecke was one of the signatories of the professors' commitment to Hitler in 1933 (the way in which this list came about in Hamburg and what exactly was signed is controversial), but was known at the university because of his critical attitude towards the National Socialists. During the Second World War he was in constant danger of being arrested because of his openly displayed anti-National Socialist attitude. Due to the poor supply situation in war-torn Hamburg in Denmark, he spent the immediate post-war period with Harald Bohr , where he died in 1947 - already marked by a long illness. Hecke was very close to some of his Hamburg colleagues, such as the physicist Otto Stern , the astronomer Walter Baade and the physicist Wolfgang Pauli . After learning of Hecke's death, the latter wrote to his widow: “But for those who stayed behind it is very sad. You know how much the personal relationship with your husband has meant to me since those very happy days in Hamburg. It was a human relationship that went far beyond common spiritual and scientific interest. There was something in common in the emotional attitude towards people and life. [...] 'In an advanced hour' (as he used to say), which we often spent with Moselle wine and music, sometimes even walking until sunrise, there was talk of more intimate things, which even touched the religious sphere. "

In 1917, Hecke showed that the Dirichlet zeta function (now called the Dedekind zeta function ) of algebraic number fields (there defined analogously to the Riemann ζ function , only the sum over the norms of the whole ideals not equal to 0) can be analytically continued in the whole complex number level (variable s) is, satisfies a functional equation and has a first-order pole at s = 1 . Like Riemann in the classical case, he uses a representation as a theta function (here in two variables). Also in 1917 he transferred this to L-functions of algebraic number fields (zeta functions with " size characters ", which generalize Dirichlet's characters, "Hecke zeta function"). In 1918 he shows a lower limit for the asymptotic behavior of the class numbers from the position of the zeros of the zeta function for imaginary quadratic number fields , which is followed by a whole series of other works by Carl Ludwig Siegel , Hans Heilbronn and others. a. followed.

In 1926 he introduced new elliptical module functions of a higher level and showed a fundamental connection ( Hecke correspondence ) with the associated Dirichlet series , which was expressed in the existence of a functional equation. The connection between modular forms and number theory is a central research area of ​​mathematics in the Langlands program today (see also Hecke operator ).

Hecke also examined the connection between modular and square forms, which, like many other works by Hecke, was taken up and expanded by Carl Ludwig Siegel .

The Hecke operators introduced by him in 1937 are named after him, they are special linear operators (matrices) on the vector space of modular forms. Their eigenfunctions are precisely those module forms whose associated Dirichlet series have an Euler product representation (see the article Hecke operator). As Hecke had previously shown the transfer of the functional equation between module forms and Dirichlet series (Hecke correspondence), the transfer of the Euler product representation is examined here (a kind of “prime number” analog in the space of module functions). The Hecke operators can already be found implicitly in the work of Louis Mordell on the Ramanujan tau function .

Hecke also wrote a number of papers on integral equations in kinetic gas theory .

In 1936 he gave a plenary lecture at the International Congress of Mathematicians in Oslo (recent advances in the theory of elliptical modular functions). In 1923 he was President of the German Mathematicians Association .

Hecke's scientific papers are kept by the Central Archives of German Mathematicians' papers at the Lower Saxony State and University Library in Göttingen .

His doctoral students include Heinrich Behnke , Bruno Schoeneberg , Hans Petersson , Hans Maaß , Kurt Reidemeister , Wilhelm Maak . In 1918 he was elected a corresponding member of the Göttingen Academy of Sciences and in 1943 a member of the Leopoldina .

Fonts

literature

  • Siegfried Gottwald , Hans Joachim Ilgauds, Karl-Heinz Schlote : Lexicon of important mathematicians. 2nd Edition. German, Thun, Frankfurt am Main 2006, ISBN 978-3-8171-1729-1 .
  • Wilhelm Maak : Erich Hecke as a teacher (commemorative speech May 23, 1947), Abh. Math. Sem. Universität Hamburg, Volume 16, Issue 1/2
  • Alexander Odefey, Elena Roussanova: Directory of the academic legacy of Erich Hecke (1887-1947). In: Communications from the Mathematical Society in Hamburg. 25, 2006, pp. 85-102.
  • Samuel Patterson : Erich Hecke and the role of the L-series in number theory. In: Hirzebruch, Fischer (ed.): A century of mathematics. Vieweg, 1990.
  • Hans Rohrbach :  Hecke, Erich. In: New German Biography (NDB). Volume 8, Duncker & Humblot, Berlin 1969, ISBN 3-428-00189-3 , p. 177 ( digitized version ).
  • Bruno Schoeneberg: Erich Hecke. In: Annual report of the German Mathematicians Association. , Vol. 91, 1989, pp. 168-190
  • Horst Tietz : Experienced history. In: Communications DMV. No. 4, 1999 (on Hecke in the “Third Reich”).

Web links

Individual evidence

  1. ↑ Confession of the professors at the German universities and colleges to Adolf Hitler and the National Socialist state . 1933, p. 129 ( archive.org ).
  2. ↑ Hans Fischer: Ethnology. In: Eckart Krause, Ludwig Huber, Holger Fischer (eds.): Everyday university life in the “Third Reich”. The Hamburg University 1933–1945. Dietrich Reimer Verlag, Berlin and Hamburg 1991, vol. 2, p. 597
  3. ↑ In his office, according to Tietz, hung the letter from a butcher master who, in response to the rejection of his attempt to square the circle with reference to Lindemann's proof of the transcendence of Pi, said: "Nothing is impossible for the German spirit"
  4. ^ Karl von Meyenn (Ed.) Wolfgang Pauli. Scientific correspondence with Bohr, Einstein, Heisenberg and others a. , Volumes I-IV. Berlin: Springer 1979-2005, Volume III, p. 422.
  5. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 107.
personal data
SURNAME Hecke, Erich
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH September 20, 1887
PLACE OF BIRTH Poses
DATE OF DEATH February 13, 1947
Place of death Copenhagen