Far Eastern Mathematical Journal

To content of the issue


On the distribution of integer points on a hyperboloid


Bykovskii V.A.

2017, issue 2, Ñ. 147-151


Abstract
A new method for studying integer points on hyperboloids (Linnik problem) is proposed. It is based on the spectral theory of automorphic functions. In doing so an asymptotic formula with a fundamentally new power saving error term is obtained.

Keywords:
distribution of integer points on a hyperboloid, spectral theory of automorphic functions, L-series of automorphic forms, Shintani correspondence

Download the article (PDF-file)

References

[1] Iu. V. Linnik, Ergodicheskie svoistva algebraicheskikh polei, Leningrad, 1967, 208 s.
[2] D.A. Burgess, “On character sums and L-series. II”, Proc. Lond. Math. Soc., 13, (1963), 524–536.
[3] H. Ivaniec, “Fourier coefficients of modular forms of half integral weight”, Invent. Math., 87, (1987), 385–402.
[4] W.J. Duke, J. Friedlander, H. Ivaniec, “Bounds for automorphic L-function”, Invent. Math., 112:1, (1993), 1–8.
[5] V.A. Bykovskii, “A trace formula for the scalar product of Hecke series and its applications”, J. Math. Sci., 89:1, (1998), 915–932.
[6] B. Conrey, H. Ivaniec, “The cubic moment of central values of automorphic L-functions”, Ann. of Math. Second Series, 151:3, (2000), 1175–1216.
[7] V.A. Bykovskii, Nekotorye formuly summirovaniia arifmeticheskogo tipa i ikh prilozheniia, Preprint, Vychislitel'nyi tsentr DVNTs AN SSSR, Vladivostok, 1986, 38 s.

To content of the issue