Geodesic
Lattice points in many-dimensional balls
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 261-274
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $P_k(n)$ be the difference of the number of points of the integer lattice contained in the ball $y_1^2+\dots+y_k^2\leq n$ and the volume of this ball. We investigate the asymptotic behavior of the sums $\sum_{n\leq x}P_k(n)$, $(k\geq4)$, $\sum_{n\leq x}P_3^2(n)$, and $\sum_{n\leq x}P_4^2(n)$ as $x\to+\infty$. 
@article{ZNSL_2016_449_a12,
     author = {O. M. Fomenko},
     title = {Lattice points in many-dimensional balls},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {261--274},
     year = {2016},
     volume = {449},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/}
}
TY  - JOUR
AU  - O. M. Fomenko
TI  - Lattice points in many-dimensional balls
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 261
EP  - 274
VL  - 449
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/
LA  - ru
ID  - ZNSL_2016_449_a12
ER  - 
%0 Journal Article
%A O. M. Fomenko
%T Lattice points in many-dimensional balls
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 261-274
%V 449
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/
%G ru
%F ZNSL_2016_449_a12
O. M. Fomenko. Lattice points in many-dimensional balls. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 261-274. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/

[1] O. M. Fomenko, “Tselye tochki v kruge i share”, Zap. nauchn. semin. POMI, 418, 2013, 198–220

[2] A. Walfisz, Weylsche Exponentialsummen in der Neueren Zahlentheorie, Berlin, 1963 | MR

[3] E. Landau, Ausgewählte Abhandlungen zur Gitterpunktlehre, Berlin, 1962 | MR

[4] A. Z. Valfish, Tselye tochki v mnogomernykh sharakh, Tbilisi, 1959

[5] S. D. Adhikari, Y.-F. S. Pétermann, “Lattice points in ellipsoids”, Acta Arithm., 59 (1991), 329–338 | MR | Zbl

[6] V. Jarnik, “Über die Mittelwertsätze der Gitterpunktlehre, 5 Abhandlung”, Časopis pro pěst. mat. a fys., 69 (1940), 148–174 | MR | Zbl

[7] Y.-K. Lau, “On the mean square formula of the error term for a class of arithmetical functions”, Monatsh. Math., 128 (1999), 111–129 | DOI | MR | Zbl

[8] V. Jarnik, “Sur une fonction arithmétique”, Věstnik Král. Čes. Sp. Nauk, 1930, 1–13

[9] K. Ramachandra, A. Sankaranarayanan, “Hardy's theorem for zeta-functions of quadratic forms”, Proc. Indian Acad. Sci. (Math. Sci.), 106:3 (1996), 217–226 | DOI | MR | Zbl

[10] M. Abramovich, I. Stigan, Spravochnik po spetsialnym funktsiyam, M., 1979

[11] E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd edn, revized by D. R. Heath-Brown, New York, 1986 | MR

[12] J. L. Hafner, “On the representation of the summatory function of a class of arithmetical functions”, Analytic Number Theory, Springer Lect. Notes Math., 899, ed. M. I. Knopp, 1981, 148–165 | DOI | MR | Zbl

[13] Y.-K. Lau, K.-M. Tsang, “Large values of error terms of a class of arithmetical functions”, J. reine angew. Math., 544 (2002), 25–38 | MR | Zbl

[14] K. Chandrasekharan, R. Narasimhan, “Hecke's functional equation and arithmetical identities”, Ann. Math., 74 (1961), 1–23 | DOI | MR | Zbl

[15] K. Chandrasekharan, R. Narasimhan, “Functional equations with multiple gamma factors and the average order of arithmetical functions”, Ann. Math., 76 (1962), 93–136 | DOI | MR | Zbl