Cihan Sabuncu

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math.NT2026

The multiplication table problem in large dimensions

Cihan Sabuncu, Christian Táfula

For $N \geq 2$ and $k \geq 1$ , let $M_{k} (N) := # {x_{1} \dots x_{k} : x_{i} \in {1, \dots, N} for all i}$ be the $k$ -dimensional multiplication table. Given $N$ , Khovanskii's theorem…

math.NT2026

Ranks of Elliptic Curves Twisted by Quadratic Forms

Mohammad H. Hamdar, Cihan Sabuncu

Let $E$ be an elliptic curve over $Q$ and let $E^{d}$ be its twist by the quadratic character $χ_{d}$ . We prove there are infinitely many twists $d$ which are sums of two squa…

math.NT2026

Missing digits and sums of two prime squares

Cihan Sabuncu

We investigate integers whose base $g$ expansion omits a fixed digit and which can be represented as a sum of two prime squares. In the first part of the paper, we apply the Hardy-…

math.NT2024

On extreme values of $r_{3} (n)$ in arithmetic progressions

Michael Filaseta, Jonah Klein, Cihan Sabuncu

For a given integer $m$ and any residue $a (mod m)$ that can be written as a sum of 3 squares modulo $m$ , we show the existence of infinitely many integers $n \equiv a (mod m)$ s…

math.NT2024

Visiting early at prime times

Tony Haddad, Sun-Kai Leung, Cihan Sabuncu

Given an integer $m \geq 2$ and a sufficiently large $q$ , we apply a variant of the Maynard--Tao sieve weight to establish the existence of an arithmetic progression with common di…

The multiplication table problem in large dimensions

Ranks of Elliptic Curves Twisted by Quadratic Forms

Missing digits and sums of two prime squares

On extreme values of r3​(n) in arithmetic progressions

Visiting early at prime times

On extreme values of $r_{3} (n)$ in arithmetic progressions