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arXiv · 1201.4341

Congruences for Convolutions of Hilbert Modular Forms

Thomas Ward
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Abstract

Let $\f$ be a primitive, cuspidal Hilbert modular form of parallel weight. We investigate the Rankin convolution $L$-values $L(\f,\g,s)$, where $\g$ is a theta-lift modular form corresponding to a finite-order character. We prove weak forms of Kato's `false Tate curve' congruences for these values, of the form predicted by conjectures in non-commmutative Iwasawa theory.

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Thomas Ward. 2012-01-20. Congruences for Convolutions of Hilbert Modular Forms. https://doi.org/10.1017/s0305004112000229

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