6 papers
Average twin prime conjecture for elliptic curves in arithmetic progressions
Ahmet M. Güloğlu, Asimina S. Hamakiotes, Sung Min Lee +1
In 1988, Koblitz conjectured an asymptotic formula for the number of primes for which the reduction of an elliptic curve over has prime order. Building on th…
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 of pairs o…
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…
Ordinary primes for -type abelian varieties and weight modular forms
Tian Wang, Pengcheng Zhang
Let be a -dimensional abelian variety defined over a number field . It is conjectured that the set of ordinary primes of over has positive density, and this is kn…
Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves
Sung Min Lee, Jacob Mayle, Tian Wang
The cyclicity and Koblitz conjectures ask about the distribution of primes of cyclic and prime-order reduction, respectively, for elliptic curves over . In 1976, Serre…
Distribution of supersingular primes for abelian surfaces
Tian Wang
Let be an absolutely simple abelian surface defined over a number field . We give unconditional upper bounds for the number of prime ideals of with norm…