Far Eastern Mathematical Journal

To content of the issue


On Gauss and Kloosterman sums


Avdeeva M.O., Gorbatuk N.V., Shulga N.A.

2020, issue 1, P. 9–14
DOI: https://doi.org/10.47910/FEMJ202002


Abstract
In this paper we calculate averages by parameters of Kloosterman sums, which include Dirichlet characters. They appear when constructing arithmetic trace formulas in the theory of automorphic forms.

Keywords:
Dirichlet characters, Gauss sums, Kloosterman sums

Download the article (PDF-file)

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] R. A. Smith, “A generalization of Kuznetsov’s identity for Kloosterman sums”, C.R. Math. Rep. Acad. Sci., 11:6, (1980), 315–320.
[5] A. V. Ustinov, “O chisle reshenii sravneniia xy ? l (mod q) pod grafikom dvazhdy nepreryvno differentsiruemoi funktsii” , Algebra i analiz, 20:5, (2008), 186–216.
[6] T. Estermann, “On Kloosterman’s sum”, Mathematika, 8:1, (1961), 83–86.
[7] G. Devenport, Mul'tiplikativnaia teoriia chisel, Nauka, M., 1971, 200 s.

To content of the issue