Hecke operators and periods of modular forms

Zagier, Don

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Hecke operators and periods of modular forms

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Zagier, Don
Max Planck Institute for Mathematics, Max Planck Society;

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引用

Zagier, D. (1990). Hecke operators and periods of modular forms. In Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part II - Papers in analysis, number theory and automorphic L-functions (pp. 321-336). The Weizmann science press of Israel.

引用: https://hdl.handle.net/21.11116/0000-0004-3936-0

要旨

[For the entire collection see Zbl 0698.00021.] \\par Let M\\sb k be the space of modular forms of weight k\\in \\bbfN on SL\\sb 2(\\bbfZ) and let T\\sbℓ(ℓ \\in \\bbfN) be the ℓ- th Hecke operator on M\\sb k. The main result of the paper is a new proof for the Eichler-Selberg trace formula giving tr(T\\sbℓ,M\\sb k), using the theory of periods of modular forms. It is remarkable that the formula one obtains in this way looks rather different from the usual one: for example, class numbers of imaginary quadratic fields do not occur explicitly.