Author

Cihan Sabuncu

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Preprint Aug 2026

The multiplication table problem in large dimensions

For $N\geq 2$ and $k\geq 1$, let $M_k(N):=\#\{x_1\cdots x_k : x_i\in\{1,\ldots,N\}\text{ for all } i\}$ be the $k$-dimensional multiplication table. Given $N$, Khovanskii's theorem implies that $M_k(N)$ agrees, for all sufficiently large $k$, with a polynomial in $k$ of degree $\pi(N)$. We determine the asymptotic size...

Cihan Sabuncu, Christian Táfula · 0 citations

Preprint Jul 2026

Ranks of Elliptic Curves Twisted by Quadratic Forms

Let $E$ be an elliptic curve over $\mathbb{Q}$ and let $E^d$ be its twist by the quadratic character $\chi_d$. We prove there are infinitely many twists $d$ which are sums of two squares such that $E^d$ has rank $1$. This result is achieved using moments of derivatives of modular $L$-functions, and particularly capture...

Mohammad H. Hamdar, Cihan Sabuncu · 0 citations