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arXiv · 2309.11207

Squares of toric period integrals in higher cohomology

Santiago Molina Blanco
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Abstract

Thanks to the Harder-Eichler-Shimura isomorphism we can realize a quaternionic automorphic representation of a fixed weight in the cohomology space of certain arithmetic groups. For many interesting applications, it is convenient to consider the cap-product of a cohomology class in these spaces with a fundamental class associated to a maximal torus. In a recent paper, the author computes the absolute value of such a cap-product, and he relates it to special values of Rankin-Selberg L-functions. This provides a formula analogous to that of Waldspurger in higher cohomology. In this paper we compute the square of the cap-product instead of its absolute value.

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Santiago Molina Blanco. 2023-09-20. Squares of toric period integrals in higher cohomology. https://arxiv.org/abs/2309.11207

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