We provide upper bounds for the mean square integral
where and lies in a suitable range. For a fixed integer, is the error term in the asymptotic formula for the summatory function of the divisor function , generated by .
On donne des estimations pour la moyenne quadratique de
où et se trouve dans un intervalle convenable. Pour un entier fixé, et le terme d’erreur pour la fonction sommatoire de la fonction des diviseurs , generée par .
@article{JTNB_2009__21_2_251_0, author = {Ivi\'c, Aleksandar}, title = {On the mean square of the divisor function in short intervals}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {251--261}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {2}, year = {2009}, doi = {10.5802/jtnb.669}, mrnumber = {2541424}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.669/} }
TY - JOUR AU - Ivić, Aleksandar TI - On the mean square of the divisor function in short intervals JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 251 EP - 261 VL - 21 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.669/ DO - 10.5802/jtnb.669 LA - en ID - JTNB_2009__21_2_251_0 ER -
%0 Journal Article %A Ivić, Aleksandar %T On the mean square of the divisor function in short intervals %J Journal de théorie des nombres de Bordeaux %D 2009 %P 251-261 %V 21 %N 2 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.669/ %R 10.5802/jtnb.669 %G en %F JTNB_2009__21_2_251_0
Ivić, Aleksandar. On the mean square of the divisor function in short intervals. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, pp. 251-261. doi : 10.5802/jtnb.669. http://archive.numdam.org/articles/10.5802/jtnb.669/
[1] G. Coppola, S. Salerno, On the symmetry of the divisor function in almost all short intervals. Acta Arith. 113(2004), 189–201. | EuDML | MR | Zbl
[2] A. Ivić, The Riemann zeta-function. John Wiley & Sons, New York, 1985 (2nd ed., Dover, Mineola, N.Y., 2003). | MR | Zbl
[3] A. Ivić, On the divisor function and the Riemann zeta-function in short intervals. To appear in the Ramanujan Journal, see arXiv:0707.1756. | Zbl
[4] M. Jutila, On the divisor problem for short intervals. Ann. Univer. Turkuensis Ser. A I 186 (1984), 23–30. | MR | Zbl
[5] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions. J. Reine Angew. Math. 313 (1980), 161–170. | EuDML | MR | Zbl
[6] E.C. Titchmarsh, The theory of the Riemann zeta-function (2nd ed.). University Press, Oxford, 1986. | MR | Zbl
[7] W. Zhang, On the divisor problem. Kexue Tongbao 33 (1988), 1484–1485. | MR
Cited by Sources: