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The Eichler-Selberg Trace Formula For Level-One Hecke Operators, Alex Barron

Honors Theses

This paper explains the steps involved in the proof of the Eichler-Selberg Trace Formula for Hecke operators of level one. It is based on an appendix in Serge Lang's Introduction to Modular Forms written by Don Zagier, though I also draw heavily from sections of Toshitsune Miyake's Modular Forms and Xueli Wang's and Dingyi Pei's Modular Forms with Integral and Half-Integral Weights.

Section 2 summarizes the necessary background in the theory of modular forms. The material covered here is standard, so I've left out most of the details and proofs. Most of the section is based on Chapter VII of …