In mathematics, the Herglotz–Zagier function, named after
Gustav Herglotz
Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian physicist best known for his works on the theory of relativity and seismology.
Biography
Gustav Ferdinand Joseph Wenzel Herglotz was born in Volary num. 28 to a public not ...
and
Don Zagier
Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the ''Col ...
, is the function
:
introduced by who used it to obtain a
Kronecker limit formula In mathematics, the classical Kronecker limit formula describes the constant term at ''s'' = 1 of a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more compli ...
for
real quadratic field
In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers.
Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 ...
s.
References
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{{DEFAULTSORT:Herglotz-Zagier function
Special functions