Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-28T18:50:51.451Z Has data issue: false hasContentIssue false
  • English
  • Français

On conjecture of Resnikoff and Saldaña

Published online by Cambridge University Press:  17 April 2009

Winfried Kohnen
Winfried Kohnen
Affiliation:
Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1974 Resnikoff and Saldaña made a remarkable conjecture about the growth of the Fourier coefficients of a Siegel cusp form F of arbitrary genus g ≥ 1. In the present note, we point out that this conjecture is at least true on average.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 235 - 237
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Böcherer, S. and Raghavan, S., ‘On Fourier coefficients of Siegel modular forms’, J. Reine Angew. Math. 384 (1988), 80–101.Google Scholar
[2]Eichler, M. and Zagier, D., The theory of Jacobi forms, Progr. Math. 55 (Birkhäuser, Boston, 1985).CrossRefGoogle Scholar
[3]Kitaoka, Y., ‘Two theorems on the class number of positive definite quadratic forms’, Nagoya Math. J. 51 (1973), 79–89.CrossRefGoogle Scholar
[4]Resnikoff, H.L. and Saldaña, R.L., ‘Some properties of Fourier coefficients of Eisenstein series of degree two’, J. Reine Angew. Math. 265 (1974), 90–109.Google Scholar
[5]Segel, C.L., ‘Über die Classenzahl quadratischer Zahlkörper’, in Collected Works I, (Chandrasekharan, K. and Maass, H., Editors) (Springer-Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
[6]Vignerás, M.-F., ‘Facteurs gamma et équations fonctionelles’, in Modular functions of one variable VI, (Serre, J.-P. and Zagier, D., Editors), Lecture Notes in Mathematics 627 (Springer-Verlag, Berlin, Heidelberg, New York, 1977), pp. 79–103.CrossRefGoogle Scholar