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L-functions and higher order modular forms

David W. Farmer·Sarah Zubairy
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Abstract

It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain cases one can associate a kind of ``higher order modular form'' to such Dirichlet series. This suggests a possible approach to a proof of the conjecture.

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David W. Farmer, Sarah Zubairy. 2006-01-07. L-functions and higher order modular forms. https://arxiv.org/abs/math/0601143

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