The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification

Yunjian Peng

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arXiv · 2511.20488

The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification

Yunjian Peng

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Abstract

In this paper, we establish the Weyl bound for the Rankin-Selberg $L$-function in a certain joint ramification setting. To achieve this result, we employ the refined Petersson trace formula and develop a special Vorono\"i summation formula. Additionally, we obtain the sharp bound for the integral of products of Whittaker functions via the $p$-adic stationary phase method.

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Yunjian Peng. 2025-11-25. The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification. https://arxiv.org/abs/2511.20488

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