Formulas for moments of class numbers in arithmetic progressions

TL;DR

This paper derives explicit formulas for the second moments of Hurwitz class numbers in specific arithmetic progressions, advancing understanding of their distribution and properties in number theory.

Contribution

It provides the first explicit formulas for second moments of Hurwitz class numbers in fixed residue classes modulo 3.

Findings

Explicit formulas for second moments of Hurwitz class numbers in arithmetic progressions

Enhanced understanding of distribution of class numbers in residue classes

Potential applications to related problems in algebraic number theory

Abstract

In this paper, we obtain explicit formulas for the second moments for Hurwitz class numbers $H(4n-t^2)$ with $t$ running through a fixed congruence class modulo $3$.