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arXiv · 2503.21648

On triple product $L$-functions and the fiber bundle method

Jayce R. Getz·Miao Pam Gu·Chun-Hsien Hsu·Spencer Leslie
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Abstract

We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product $L$-function times a product of $L$-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show how it implies the analytic properties of triple product $L$-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a simpler case of the Poisson summation conjecture along with certain local compatibility statements.

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Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu, Spencer Leslie. 2025-03-27. On triple product $L$-functions and the fiber bundle method. https://arxiv.org/abs/2503.21648

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