Trace formulas and class number sums
Number Theory
2007-05-23 v1
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.
Cite
@article{arxiv.math/0610959,
title = {Trace formulas and class number sums},
author = {Nathan Jones},
journal= {arXiv preprint arXiv:math/0610959},
year = {2007}
}
Comments
21 pages