Trace formulas and class number sums

Details Trace formulas and class number sums Trace formulas and class number sums

2006-10-31

arxiv.org/abs/math/0610959v1

Mathematics

Number Theory

21 pages

Scientific paper

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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