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VOL. 86 | 2020 On primitive $p$-adic Rankin-Selberg $L$-functions
Shih-Yu Chen, Ming-Lun Hsieh

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Abstract

In this note, we revisit Hida's construction of $p$-adic Rankin-Selberg $L$-functions by incorporating Jacquet's approach to automorphic $L$-functions on $\mathrm{GL}(2) \times \mathrm{GL}(2)$. This allows us to give a construction of primitive three variable $p$-adic Rankin-Selberg $L$-functions associated with a pair of two primitive Hida families in full generality and prove the functional equation of this $p$-adic Rankin-Selberg $L$-function.

Information

Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610195

Subjects:
Primary: 11F33 , 11F67

Keywords: $p$-adic $L$-functions , Rankin-Selberg method

Rights: Copyright © 2020 Mathematical Society of Japan

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