30 citations · 37 across the 10 of their papers we have counts for
19 papers · 1 filter
A proof of Sylvester's conjecture
Ashay Burungale, Ye Tian
We prove Sylvester's conjecture, originating in his 1879 study of ternary cubic equations, that every prime is a sum of two rational cubes. Elkies announced a…
Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura +1
We propose an integral framework for the anticyclotomic Iwasawa theory of CM elliptic curves at primes ramified in the CM field. The -constants of the geometri…
A refined non-vanishing of the -adic logarithm of a rational point on an abelian variety
Ashay Burungale, Christopher Skinner, Xin Wan
Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna -- the oft-termed BDP formula -- we address questions about the non-vanishing of non-torsion points under -adi…
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…