A trace formula expressing the mean values of the form (k = 2, 3,... ) ! via certain arithmetic means on the group F0(N1 ) is proved. Here the sum is taken over a normalized orthogonal basis in the space of holomorphic cusp forms of weight 2k with respect to F0(N1).

of the form HiTi, where each T i is contained in Lm(q) and is a linear combination of left classes of integral matrices of identical factors Di = Pi di" Then applying formula (8) successively for each T i (this can be done since the determinant, the level, and the signature of each of the matrices ~ [~] in the right-hand side are the same as for Q), we obtain that the formula (12) is valid with some constant coefficients r independent of n.

No abstract

АннотацияNew uniform asymptotic formulas are obtained for the second moment of L-series of cusp forms of even weight 2k 2 with respect to the congruence subgroup Γ 0 (N ).

No abstract