Traces of Hecke Operators: Volume 10
Andrew Knightly · Charles Li
Jan 2006 · Mathematical Surveys and Monographs Book 133 · American Mathematical Soc.
Ebook
378
Pages
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About this ebook
The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formula for the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The book concludes with several applications of the final formula.
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