Abstract
For 1/2<σ<1 fixed, letE σ(T) denote the error term in the asymptotic formula for\(\int_0^T {|\zeta (\sigma + it)|^2 dt} \). We obtain some new bounds forE σ(T), and an Ω_-result which is the analogue of the strongest Ω_-result in the classical Dirichlet divisor problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atkinson, F. V.: The mean-value of the Riemann zeta function. Acta Math.81, 353–376 (1949).
Balasubramanian, R., Ivić, A., Ramachandra, K.: The mean square of the Riemann zeta-function on the line σ=1. L'Enseignement Math.38, 13–25 (1992).
Bombieri, E., Iwaniec, H.: On the order of ζ(1/2+it). Ann. Scuola Norm. Sup. Pisa (4)13, 449–472 (1986).
Bombieri, E., Iwaniec, H.: Some mean-value theorems for exponential sums. Ann. Scuola Norm. Sup. Pisa (4)13, 473–486 (1986).
Corrádi, K., Kátai, I.: Egy megjegyzés K. S. Gangadharan “Two classical lattice point problems” című dolgozatához, MTA III Ostály Közlemenyei17, 89–97 (1967).
Gangadharan, K. S.: Two classical lattice point problems. Proc. Cambridge Phil. Soc.57, 699–721 (1961).
Graham, S. W., Kolesnik, G.: Van der Corput's method of exponential sums. Cambridge: Univ. Press. 1991.
Hafner, J. L.: New omega results in a weighted divisor problem. J. Number Theory28, 240–257 (1988).
Hafner, J. L., Ivić, A.: On the mean-square of the Riemann zeta-function on the critical line. J. Number Theory32, 151–191 (1989).
Huxley, M. N.: Exponential sums and the Riemann zeta-function IV. Proc. London Math. Soc. (3)66, 1–40 (1993).
Huxley, M. N., Watt, N.: Exponential sums and the Riemann zeta-function. Proc. London Math. Soc. (3)57, 1–24 (1988).
Ingham, A. E.: On two classical lattice point problems. Proc. Cambridge Phil. Soc.36, 131–138 (1940).
Ivić, A.: The Riemann zeta-function. New York: Wiley, 1985.
Ivić, A.: Mean values of the Riemann zeta function. Lecture Note Ser. 82. Tata Institute of Fundamental Research, Bombay. Berlin-Heidelberg-New York: Springer. 1991.
Ivić, A.: La valeur moyenne de la fonction zeta de Riemann. In: (S. David, ed.) Séminaire de Théorie des Nombres, Paris, 1990–1991, pp. 115–125. Boston: Birkhäuser. 1993.
Matsumoto, K.: The mean square of the Riemann zeta-function in the critical strip. Japanese J. Math.15, 1–13 (1989).
Matsumoto, K., Meurman, T.: The mean square of the Riemann zeta-function in the critical strip II. Acta Arith.68, 369–382 (1994); III, Acta Arith.64, 357–382 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ivić, A., Matsumoto, K. On the error term in the mean square formula for the Riemann zeta-function in the critical strip. Monatshefte für Mathematik 121, 213–229 (1996). https://doi.org/10.1007/BF01298951
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01298951