arXiv subjects

Ahmet M. Güloğlu

Publications and source records attributed to Ahmet M. Güloğlu.

2 recordsLinked to original sources

arXiv2026

Average twin prime conjecture for elliptic curves in arithmetic progressions

In 1988, Koblitz conjectured an asymptotic formula for the number of primes $p \le x$ for which the reduction of an elliptic curve over $\mathbb{Q}$ has prime order. Building on the work of Balog, Cojocaru, and David, who proved this conjecture on average in 2011, we extend the result to primes $p$ lying in arithmetic progressions. Our asymptotic formula holds uniformly for moduli up to a fixed power of $\log x$. We also show that the resulting average constant matches the theoretical constant predicted by Lee, Mayle, and Wang in 2025 using Galois representations.

math.NT↗

arXiv2023

Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field

We prove, assuming the generalized Riemann Hypothesis (GRH) that there is a positive density of $L$-functions associated with primitive cubic Dirichlet characters over the Eisenstein field that do not vanish at the central point $s=1/2$. This is achieved by computing the first mollified moment, which is obtained unconditionally, and finding a sharp upper bound for the higher mollified moments for these $L$-functions, under GRH. The proportion of non-vanishing is explicit, but extremely small.

math.NT↗