TY - JOUR
AB - 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.
AU - Januszewski, Fabian
ID - 53190
JF - To appear in the American Journal of Mathematics
SN - 0002-9327
TI - Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values
ER -