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arXiv · 1302.3249

Special Values of Anticyclotomic L-functions Modulo \lambda

Alia Hamieh
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Abstract

The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic $\mathbb{Z}_{p}$-extension. Let $g$ be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level $\mathcal{N}$ over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant $\mathcal{D}$. We study the $l$-adic valuation of the special values $L(g,\chi,\frac{1}{2})$ as \chi varies over the ring class characters of K of $\mathcal{P}$-power conductor, for some fixed prime ideal $\mathcal{P}$. We prove our results under the only assumption that the prime to $\mathcal{P}$ part of $\mathcal{N}$ is relatively prime to $\mathcal{D}$.

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Alia Hamieh. 2013-02-13. Special Values of Anticyclotomic L-functions Modulo \lambda. https://doi.org/10.1007/s00229-014-0696-4

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