Far Eastern Mathematical Journal

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The generalized Petersson trace formula for congruence subgroups


Avdeeva M.O.

2020, issue 1, P. 3–8
DOI: https://doi.org/10.47910/FEMJ202001


Abstract
In this paper, a generalization of the Petersson trace formula for holomorphic parabolic forms with positive even weight with respect to congruence subgroup $\Gamma_0 (N)$ of the Dirichlet character modulo $N$ is proved.

Keywords:
automorphic forms, trace formulas, Hecke operators, Kloosterman sums

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References

[1] D. R. Heath-Brown, “The Fourth Power Moment of the Riemann Zeta Function”, Proc. London Math. Soc., 38:3, (1979), 385–422.
[2] A. Selberg, “Uber die Fourierkoeffizienten elliptischen Modulformen negativer Dimension”, Neuvieme Congres Math. Scandinaves, Helsingfors, 1938, 320–322.
[3] N. V. Kuznetsov, “ Gipoteza Petersona dlia parabolicheskikh form vesa nul' i gipoteza Linnika. Summy summ Kloostermana”, Matem. sb., III (153):3, (1980), 334–383.
[4] A. I. Vinogradov, “ Ukorochennoe uravnenie dlia svertok”, Zap. nauchn. sem. POMI, 211, (1994), 104–119.
[5] J.A. Andersson, Summation formulae and zeta functions, Doctoral Dissertation, Department of mathematics Stockholm University, 2006, 107 pp.
[6] Kh. Ivanets, E. Koval'skii, Analiticheskaia teoriia chisel, MTsNMO, M, 2014, 715 s.

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