Herglotz–Zagier function

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title: "Herglotz–Zagier function" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["special-functions"] topic_path: "general/special-functions" source: "https://en.wikipedia.org/wiki/Herglotz–Zagier_function" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

In mathematics, the Herglotz–Zagier function, named after Gustav Herglotz and Don Zagier, is the function

:F(x)= \sum^{\infty}_{n=1} \left{\frac{\Gamma^{\prime}(nx)}{\Gamma (nx)} -\log (nx)\right} \frac{1}{n}.

introduced by who used it to obtain a Kronecker limit formula for real quadratic fields.

References

Über die Kroneckersche Grenzformel für reelle, quadratische Körper |volume= 75 |year=1923|pages= 3–14|jfm=49.0125.03}}

References

  1. (2004). "The Herglotz–Zagier function, double zeta functions, and values of L-series". [[Journal of Number Theory]].
  2. (1975). "A Kronecker limit formula for real quadratic fields". [[Mathematische Annalen]].

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special-functions