Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values

F. Januszewski, American Journal of Mathematics 146 (2024) 495–578.

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Journal Article | Published | English
Abstract
We prove new congruences between special values of Rankin-Selberg $L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over arbitrary number fields. This allows us to control the behavior of $p$-adic $L$-functions under Tate twists and to prove the existence of non-abelian $p$-adic $L$-functions for Hida families on $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$. As an application, we prove strong non-vanishing results for central $L$-values: We give sufficient local conditions for twisted central Rankin-Selberg $L$-values to be generically non-zero.
Publishing Year
Journal Title
American Journal of Mathematics
Volume
146
Issue
2
Page
495-578
ISSN
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Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. American Journal of Mathematics. 2024;146(2):495-578.
Januszewski, F. (2024). Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values. American Journal of Mathematics, 146(2), 495–578.
@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} }
Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” American Journal of Mathematics 146, no. 2 (2024): 495–578.
F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of  central $L$-values,” American Journal of Mathematics, vol. 146, no. 2, pp. 495–578, 2024.
Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of  Central $L$-Values.” American Journal of Mathematics, vol. 146, no. 2, Johns Hopkins University, Johns Hopkins University Press, 2024, pp. 495–578.

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