Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the refined Herglotz-Zagier function

Ziyi Huang

Abstract

We give a functional equation for the refined Herglotz-Zagier function. It is analogous to a result in the theory of modular forms.

On the refined Herglotz-Zagier function

Abstract

We give a functional equation for the refined Herglotz-Zagier function. It is analogous to a result in the theory of modular forms.
Paper Structure (5 sections, 6 theorems, 30 equations)

This paper contains 5 sections, 6 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Statement of the result
  3. Properties
  4. Proof of Theorem 1
  5. Acknowledgements

Key Result

Theorem 1

Let $l$ be a prime number. If $\theta_l$ satisfies $\mathscr{C}_l$, then we have the functional equation

Theorems & Definitions (13)

  • Definition 1
  • Example 1
  • Definition 2
  • Theorem 1
  • Corollary 1
  • Proposition 1: The 5-term relation
  • proof
  • Theorem 2: Radchenko and Zagier
  • proof
  • Corollary 2
  • ...and 3 more