---
_id: '53190'
abstract:
- lang: eng
  text: "We prove new congruences between special values of Rankin-Selberg\r\n$L$-functions
    for $\\mathrm{GL}(n+1)\\times\\mathrm{GL}(n)$ over arbitrary number\r\nfields.
    This allows us to control the behavior of $p$-adic $L$-functions under\r\nTate
    twists and to prove the existence of non-abelian $p$-adic $L$-functions\r\nfor
    Hida families on $\\mathrm{GL}(n+1)\\times\\mathrm{GL}(n)$. As an application,\r\nwe
    prove strong non-vanishing results for central $L$-values: We give\r\nsufficient
    local conditions for twisted central Rankin-Selberg $L$-values to be\r\ngenerically
    non-zero."
article_type: original
author:
- first_name: Fabian
  full_name: Januszewski, Fabian
  id: '81636'
  last_name: Januszewski
  orcid: 0000-0002-3184-237X
citation:
  ama: Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing
    of  central $L$-values. <i>American Journal of Mathematics</i>. 2024;146(2):495-578.
  apa: Januszewski, F. (2024). Non-abelian $p$-adic Rankin-Selberg $L$-functions and
    non-vanishing of  central $L$-values. <i>American Journal of Mathematics</i>,
    <i>146</i>(2), 495–578.
  bibtex: '@article{Januszewski_2024, title={Non-abelian $p$-adic Rankin-Selberg $L$-functions
    and non-vanishing of  central $L$-values}, volume={146}, number={2}, journal={American
    Journal of Mathematics}, publisher={Johns Hopkins University, Johns Hopkins University
    Press}, author={Januszewski, Fabian}, year={2024}, pages={495–578} }'
  chicago: 'Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions
    and Non-Vanishing of  Central $L$-Values.” <i>American Journal of Mathematics</i>
    146, no. 2 (2024): 495–578.'
  ieee: F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing
    of  central $L$-values,” <i>American Journal of Mathematics</i>, vol. 146, no.
    2, pp. 495–578, 2024.
  mla: Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and
    Non-Vanishing of  Central $L$-Values.” <i>American Journal of Mathematics</i>,
    vol. 146, no. 2, Johns Hopkins University, Johns Hopkins University Press, 2024,
    pp. 495–578.
  short: F. Januszewski, American Journal of Mathematics 146 (2024) 495–578.
date_created: 2024-04-03T16:55:16Z
date_updated: 2024-10-22T14:43:13Z
external_id:
  arxiv:
  - '1708.02616'
intvolume: '       146'
issue: '2'
language:
- iso: eng
page: 495-578
publication: American Journal of Mathematics
publication_identifier:
  issn:
  - 0002-9327
publication_status: published
publisher: Johns Hopkins University, Johns Hopkins University Press
status: public
title: Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central
  $L$-values
type: journal_article
user_id: '81636'
volume: 146
year: '2024'
...