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arXiv · 1612.06948

Anticyclotomic p-adic L-functions and Ichino's formula

Dan J. Collins
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Abstract

We give a new construction of a $p$-adic $L$-function $\mathcal{L}(f,\Xi)$, for $f$ a holomorphic newform and $\Xi$ an anticyclotomic family of Hecke characters of $\mathbb{Q}(\sqrt{-d})$. The construction uses Ichino's triple product formula to express the central values of $L(f,\xi,s)$ in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what happens when $f$ is replaced by a modular form congruent to it modulo $p$, and has future applications in the case where $f$ is residually reducible.

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Dan J. Collins. 2016-12-21. Anticyclotomic p-adic L-functions and Ichino's formula. https://doi.org/10.1007/s40316-019-00118-1

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