Far Eastern Mathematical Journal

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Multiplicative characteristics of function for the number of classes of primitive hyperbolic elements in the group $\Gamma_0 (N)$ by level $N$

V. V. Golovchanskii, M. N. Smotrov

2009, issue 1-2, P. 48–73

Abstract

An arithmetical forms of Selberg's trace formula and Selberg's zeta-function for the congruence subgroup $\Gamma_0 (N)$, explicit expression for the number of classes of primitive hyperbolic elements in the congruence subgroup level $N$ in terms of the number of classes of primitive elements in the congruence subgroup level $N_1=N/p^i$, $(N,N_1)=1$ and sharp upper bound of the number classes by level $N$ are obtained.

Keywords: congruence subgroup of modular group, classes of primitive hyperbolic elements, Pell's equation, Selberg's trace formula

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References

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