Hostname: page-component-7bb8b95d7b-495rp Total loading time: 0 Render date: 2024-09-19T07:56:38.660Z Has data issue: false hasContentIssue false
  • English
  • Français

On some p-adic properties of the eichler-selberg trace formula

Published online by Cambridge University Press:  22 January 2016

Masao Koike
Masao Koike*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

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 this paper we shall prove some congruence relations mod pα between the traces of Hecke operators T(pm) which act on the space of cusp forms of different weights satisfying some congruences mod pα – pα-1. The method of the proof is very simple and is applicable to all the cases where the trace formula for Hecke operators are already known.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 45 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Dwork, B., On Hecke polynomials, Inventiones Math., 12 (1971), 249–256.Google Scholar
[2] Dwork, B., The Up operator of Atkin on modular functions of level 2 with growth conditions, Modular functions of one variable III, lecture note in mathematics, Springer, Berlin-Heidelberg New York, 1973.Google Scholar
[3] Eichler, M., Zur Zahlentheorie der Quaternionen-Algebren, J. Reine Angew. Math., 195 (1956), 127–151.Google Scholar
[4] Eichler, M., Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 217–239.Google Scholar
[5] Hijikata, H., Explicit formula of the traces of Hecke operators for Γ0(N) , J. Math. Soc. of Japan, 26 (1974), 56–82.Google Scholar
[6] Ihara, Y., Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267–295.Google Scholar
[7] Koike, M., Congruences between modular forms and functions and applications to the conjecture of Atkin, J. Fac. Sci. Univ. Tokyo, Sec. IA, 20 (1973), 129–169.Google Scholar
[8] Morita, Y., Hecke polynomials (u) (p=2 or 3), J. Fac. Sci. Univ. Tokyo, Sec. I., 15 (1968), 99–105.Google Scholar
[9] Morita, Y., Hecke polynomials of modular groups, J. Math. Soc. Japan, 21 (1969), 607–637.CrossRefGoogle Scholar
[10] Serre, J.-P., Formes modulaires et fonctions zêta p-adiques, Modular functions of one variable III, lecture note in mathematics, Springer, Berlin-Heidelberg-New York, 1973.Google Scholar
[11] Shimizu, H., On traces of Hecke operators, J. Fac. Sci. Univ. Tokyo, Sec. IA, 10 (1963), 1–19.Google Scholar
[12] Atkin, A. O. L., and Lehner, J., Hecke operators on Γ0(m) , Math. Ann., 185 (1970), 134–160.Google Scholar