• Corpus ID: 229924367

# Arithmetic properties of the Herglotz function

@inproceedings{Radchenko2020ArithmeticPO,
title={Arithmetic properties of the Herglotz function},
author={Danylo V. Radchenko and Don Zagier},
year={2020}
}
• Published 31 December 2020
• Mathematics
In this paper we study two functions F (x) and J(x), originally found by Herglotz in 1923 and later rediscovered and used by one of the authors in connection with the Kronecker limit formula for real quadratic fields. We discuss many interesting properties of these functions, including special values at rational or quadratic irrational arguments as rational linear combinations of dilogarithms and products of logarithms, functional equations coming from Hecke operators, and connections with…

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