30 citations · 86 across the 26 of their papers we have counts for
5 papers · 1 filter
A local sign decomposition for symplectic self-dual Galois representations of rank two
Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura +1
We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual -adic representations of of rank two (a l…
Mod non-vanishing of self-dual Hecke -values over CM fields and applications
Ashay Burungale, Wei He, Ye Tian +1
Let be a self-dual Hecke character over a CM field . Let be a degree one prime of the maximal totally real subfield of and the Galo…
The -adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke -values of imaginary quadratic fields at inert primes
Ashay Burungale, Shinichi Kobayashi, Kazuto Ota
We prove an asymptotic formula for the -adic valuation of Hecke -values of an imaginary quadratic field at an inert prime along the anticyclotomic -tower. T…
A rank zero -converse to a theorem of Gross--Zagier, Kolyvagin and Rubin
Ashay A. Burungale, Ye Tian
Let be a CM elliptic curve defined over and a prime. We show that $${\mathrm corank}_{\mathbb{Z}_{p}} {\mathrm Sel}_{p^{\infty}}(E_{/\mathbb{Q}})=0 \implies {\…
Generation of Hecke fields by squares of cyclotomic twists of modular -values
Valentin Blomer, Ashay Burungale, Philippe Michel +1
Let be a non-CM elliptic newform without a quadratic inner twist, an odd prime and a Dirichlet character of -power order and sufficiently large -power conductor.…