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On p-adic properties of the Eichler-Selberg trace formula II

Published online by Cambridge University Press:  22 January 2016

M. Koike
M. Koike*
Affiliation:
Nagoya University
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Let be the space of cusp forms of weight k with respect to SL(2, Z). Let p be a prime number and let Tk(p) be the Hecke operator of degree p acting on as a linear endomorphism. Put Hk(X) = det (I – Tk(p)X + pk-lX2I), where I is the identity operator on . Hk(X) is a polynomial with coefficients of rational integers, which is called the Hecke polynomial.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 64 , December 1976 , pp. 87 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Ihara, Y., Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267–295.CrossRefGoogle Scholar
[2] Koike, M., On some p-adic properties of the Eichler-Selberg trace formula, Nagoya Math. J., vol. 56 (1974), 45–52.Google Scholar
[3] Serre, J.-P., Formes modulaires et fonctions zeta p-adiques, Modular functions of one variable III, Lecture note in math., Springer, Berlin-Heidelberg-New York, 1973.Google Scholar