Dimitris Koukoulopoulos

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math.NT2025

Irreducibility and Galois groups of random reciprocal polynomials of large degree

David Hokken, Dimitris Koukoulopoulos

Let $A = a_{0} T^{m} + \sum_{j = 1}^{m - 1} a_{j} (T^{m - j} + T^{m + j}) + T^{2 m} + 1 \in Z [T]$ be a monic reciprocal polynomial of degree $2 m$ sampled randomly by selecting its coefficient…

math.NT2025

Erdős's integer dilation approximation problem and GCD graphs

Dimitris Koukoulopoulos, Youness Lamzouri, Jared Duker Lichtman

Let $A \subset R_{⩾ 1}$ be a countable set such that $lim sup_{x \to \infty} \frac{1}{l o g x} \sum_{α \in A \cap [1, x]} \frac{1}{α} > 0$ . We prove that, for ev…

math.NT2019

The structure of multiplicative functions with small partial sums

Dimitris Koukoulopoulos, K. Soundararajan

The Landau-Selberg-Delange method provides an asymptotic formula for the partial sums of a multiplicative function whose average value on primes is a fixed complex number $v$ . The…

math.NT2019

On the Duffin-Schaeffer conjecture

Dimitris Koukoulopoulos, James Maynard

Let $ψ : N \to R_{\geq 0}$ be an arbitrary function from the positive integers to the non-negative reals. Consider the set $A$ of real numbers $α$ for which t…