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arXiv · 1804.04234

The basis problem revisited

Kimball Martin
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Abstract

We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general level than earlier work of Hijikata-Pizer-Shemanske for elliptic modular forms, and solves the basis problem for Hilbert modular forms. The approach is representation theoretic rather than the classical approach of Eichler and Hijikata-Pizer-Shemanske, and involves both a local and global theory of quaternionic newforms.

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Kimball Martin. 2020-06-08. The basis problem revisited. https://doi.org/10.1090/tran%2F8077

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