Far Eastern Mathematical Journal

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Eichler – Shimura – Manin Theory

V. A. Bykovskii

2009, issue 1-2, P. 29–37

Abstract

We study the category of moduli with right action of $PSL_2(\mathbb{Z})$. Analogues of modular forms (Eichler – Shimura moduli) including the theory of Hecke operators are constructed for this category.

Keywords: automorphic functions, modular symbols, Eichler – Shimura relations

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References

[1] M. Eichler, “Eine Verallgemeinerung derAbelschen Integrale”, Math. Z., 67 (1957), 267–298. [2] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press. NJ, 1971. [3] Yu. I. Manin, “Parabolicheskie formy i dzeta-funkcii modulyarnyx krivyx”, Izv. AN SSSR, ser. matem., 36 (1972), 19–66. [4] Yu. I. Manin, “Periody parabolicheskix form i p-adicheskie ryady Gekke”, Matem. sb., 92:3 (1973), 378–401. [5] Yu. I. Manin, “Explicit formulas for the eigenvalues of Hecke operators”, Acta Arith., 24 (1973), 239–249. [6] V. A. Bykovskij, “Obrazuyushhie e'lementy annuliruyushhego ideala dlya modulyarnyx simvolov”, Funkcional'nyj analiz i ego prilozheniya, 37:4 (2003), 27–38. [7] R. A. Rankin, Modular forms and function, Cambridge University Press, 1977.

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