Trace formulas and class number sums

2006/10/31 by Nathan Jones, Jones, Nathan
Mathematics · #11F32 #11R29 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F32 #msc:11R29

paper · pdf · doi:10.48550/arxiv.math/0610959

21 pages

arxiv created 2006/10/31 · openalex publication_date 2006/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the number of (weighted) SL(2,Z)-conjugation orbits of 2 by 2 matrices of determinant p whose reductions modulo N lie in a given conjugacy class in GL(2,Z/NZ). This generalizes an 1885 result of Hurwitz.

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