Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-27T14:22:10.538Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Mertens conjecture for cusp forms

Published online by Cambridge University Press:  26 February 2010

F. Grupp
F. Grupp
Affiliation:
Abteilung für Mathematik III, Universität Ulm, D-79, Ulm, Oberer Eselsberg, Germany
Get access

Extract

Let f be a non-zero cusp form of weight k on SL(2, ℤ) with Fourier expansion We assume further that f is normalized (a(1) = 1) and that f is an eigenfunction of the Hecke operators. Define

Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 213 - 226
Copyright
Copyright © University College London 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anderson, R. J.. On the Mertens conjecture for cusp forms. Mathematika, 26 (1979), 236–249.CrossRefGoogle Scholar
2.Deligne, P.. La Conjecture de Weil I. Inst. haul. Étud. sci. Publ. math., 43 (1973), 273–307.CrossRefGoogle Scholar
3.Goldstein, L. J.. A necessary and sufficient condition for the Riemann hypothesis for zeta functions attached to eigenfunctions of the Hecke operators. Acta Arith., 15 (1968/1969), 205–215.CrossRefGoogle Scholar
4.Jurkat, W. B.. On the Mertens conjecture and related general Ω-theorems. Proc. Symp. Pure Math., Analytic Number Theory, A.M.S., 24 (1973), 147–158.CrossRefGoogle Scholar
5.Lekkerkerker, C. G.. On the zeros of a class of Dirichlet-Series (Van Gorcum, Assen, 1955).Google Scholar
6.Rankin, R. A.. Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions. I. The zeros of the function on the line Re . Proc. Cambridge Phil. Soc., 35 (1939), 351–356.Google Scholar
7.Titchmarsh, E. C.. The theory of the Riemann zeta-function (Oxford, 1951).Google Scholar