Central derivatives of L-functions in Hida families

Benjamin Howard

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arXiv · 1202.6360

Central derivatives of L-functions in Hida families

Benjamin Howard

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Abstract

We prove a result of the following type: given a Hida family of modular forms, if there exists a weight two form in the family whose L-function vanishes to exact order one at s=1, then all but finitely many weight two forms in the family enjoy this same property. The analogous result for order of vanishing zero is also true, and is an easy consequence of the existence of the Mazur-Kitagawa two-variable p-adic L-function.

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Benjamin Howard. 2012-02-28. Central derivatives of L-functions in Hida families. https://arxiv.org/abs/1202.6360

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