Ye Tian

activity

20242026

most citedZeta elements for elliptic curves and applications

3 citations · 3 across the 3 of their papers we have counts for

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4 papers · 1 filter

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.NT2025

Mod $ℓ$ non-vanishing of self-dual Hecke $L$ -values over CM fields and applications

Ashay Burungale, Wei He, Ye Tian +1

Let $λ$ be a self-dual Hecke character over a CM field $K$ . Let $p$ be a degree one prime of the maximal totally real subfield $F$ of $K$ and $Γ_{p}$ the Galo…

math.NT2025

A rank zero $p$ -converse to a theorem of Gross--Zagier, Kolyvagin and Rubin

Ashay A. Burungale, Ye Tian

Let $E$ be a CM elliptic curve defined over $Q$ and $p$ a prime. We show that $${\mathrm corank}_{\mathbb{Z}_{p}} {\mathrm Sel}_{p^{\infty}}(E_{/\mathbb{Q}})=0 \implies {\…

math.NT2024★ 3 cited

Zeta elements for elliptic curves and applications

Ashay Burungale, Christopher Skinner, Ye Tian +1

Let $E$ be an elliptic curve defined over $Q$ with conductor $N$ and $p ∤ 2 N$ a prime. Let $L$ be an imaginary quadratic field with $p$ split. We prove the existence of…

A proof of Sylvester's conjecture

Mod ℓ non-vanishing of self-dual Hecke L-values over CM fields and applications

A rank zero p-converse to a theorem of Gross--Zagier, Kolyvagin and Rubin

Zeta elements for elliptic curves and applications

Mod $ℓ$ non-vanishing of self-dual Hecke $L$ -values over CM fields and applications

A rank zero $p$ -converse to a theorem of Gross--Zagier, Kolyvagin and Rubin