Ashay A. Burungale

activity

20152026

p

-adic Abel-Jacobi image of generalised Heegner cycles modulo

p

, II: Shimura curves

30 citations · 39 across the 18 of their papers we have counts for

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Showing 2026 · math.NTShow all

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math.NT2026

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 $p \equiv 4, 7, 8 (mod 9)$ is a sum of two rational cubes. Elkies announced a…

math.NT2026

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 $E$ at primes $p$ ramified in the CM field. The $ε$ -constants of the geometri…

math.NT2026

A refined non-vanishing of the $p$ -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 $p$ -adi…

A proof of Sylvester's conjecture

Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes

A refined non-vanishing of the p-adic logarithm of a rational point on an abelian variety

A refined non-vanishing of the $p$ -adic logarithm of a rational point on an abelian variety