Geodesic
Three-dimensional analogues of the Heath-Brown and Selberg identities
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 14-16 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Analogues of the Heath-Brown and Selberg identities for three-dimensional Kloosterman sums are proved.
Keywords: analytic number theory, Kloosterman sums, estimates of trigonometric sums. 
@article{DANMA_2020_494_a2,
     author = {V. A. Bykovskii and A. V. Ustinov},
     title = {Three-dimensional analogues of the {Heath-Brown} and {Selberg} identities},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {14--16},
     year = {2020},
     volume = {494},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_494_a2/}
}
TY  - JOUR
AU  - V. A. Bykovskii
AU  - A. V. Ustinov
TI  - Three-dimensional analogues of the Heath-Brown and Selberg identities
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 14
EP  - 16
VL  - 494
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_494_a2/
LA  - ru
ID  - DANMA_2020_494_a2
ER  - 
%0 Journal Article
%A V. A. Bykovskii
%A A. V. Ustinov
%T Three-dimensional analogues of the Heath-Brown and Selberg identities
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 14-16
%V 494
%U http://geodesic.mathdoc.fr/item/DANMA_2020_494_a2/
%G ru
%F DANMA_2020_494_a2
V. A. Bykovskii; A. V. Ustinov. Three-dimensional analogues of the Heath-Brown and Selberg identities. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 14-16. http://geodesic.mathdoc.fr/item/DANMA_2020_494_a2/

[1] Smith R.A., “The generalized divisor problem over arithmetic progressions”, Mathematische Annalen, 260 (1982), 255–268 | DOI | MR | Zbl

[2] Heath-Brown D.R., “The fourth power moment of the Riemann zeta function”, Proc. London Mathematical Society, 38:3 (1979), 385–422 | DOI | MR | Zbl

[3] Selberg A., “Über die Fourierkoeffizienten elliptischer Modulformen negativer Dimension”, Neuvième Congrès Math Scandinaves, Helsinki, 1938, 320–322

[4] Kuznetsov N.V., “Gipoteza Petersona dlya parabolicheskikh form vesa nul i gipoteza Linnika. Summy summ Klostermana”, Matem. sb., 111(153):3 (1980), 334–383 | MR | Zbl

[5] Smith R.A., “A generalization of Kuznietsov's identity for Kloosterman sums”, C.R. Math. Rep. Acad. Sci. Canada, 2:6 (1980), 315–320 | MR | Zbl

[6] Ustinov A.V., “O chisle reshenii sravneniya $xy \equiv l \pmod q$ pod grafikom dvazhdy nepreryvno differentsiruemoi funktsii”, Algebra i analiz, 20:5 (2008), 186–216

[7] Estermann T., “On Kloosterman's sum”, Mathematika, 8 (1961), 83–86 | DOI | MR | Zbl

[8] Smith R.A., “On $n$-dimensional Kloosterman sums”, J. Number Theory, 11 (1979), 324–343 | DOI | MR | Zbl