Tian Wang

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20242026

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math.NT2025

Effective open image theorem and a Linnik type problem for elliptic curves

Tian Wang, Zhining Wei

We study an effective open image theorem for families of elliptic curves and products of elliptic curves ordered by conductor. Unconditionally, we prove that for $100%$ of pairs o…

math.NT2025

Rational points on varieties defined by multihomogeneous diagonal forms

Doyon Kim, Tian Wang

We give an asymptotic formula for the number of rational points of bounded height on algebraic varieties defined by systems of multihomogeneous diagonal equations. The proof uses t…

math.NT2025

Ordinary primes for $GL_{2}$ -type abelian varieties and weight $2$ modular forms

Tian Wang, Pengcheng Zhang

Let $A$ be a $g$ -dimensional abelian variety defined over a number field $F$ . It is conjectured that the set of ordinary primes of $A$ over $F$ has positive density, and this is kn…

Effective open image theorem and a Linnik type problem for elliptic curves

Rational points on varieties defined by multihomogeneous diagonal forms

Ordinary primes for GL2​-type abelian varieties and weight 2 modular forms

Ordinary primes for $GL_{2}$ -type abelian varieties and weight $2$ modular forms