Dimitris Koukoulopoulos

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20242026

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math.NT2026

A logarithmic structure theorem for multiplicative functions with small partial sums

Dimitris Koukoulopoulos

Let $D \in N$ , let $A > D + 1$ , and let $Q ⩾ 3$ . Consider the class of multiplicative functions $f : N \to C$ such that $|\sum_{n\leqslant x}f(n)|\le x(\log…

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

On Arratia's coupling and the Dirichlet law for the factors of a random integer

Tony Haddad, Dimitris Koukoulopoulos

Let $x \geq 2$ , let $N_{x}$ be an integer chosen uniformly at random from the set $Z \cap [1, x]$ , and let $(V_{1}, V_{2}, \dots)$ be a Poisson--Dirichlet process of parameter $1…

math.NT2025

ErdÅs'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 $lim sup_{x \to \infty} \frac{1}{l o g x} \sum_{I^\pm \in A \cap [1, x]} \frac{1}{I ^} \pm > 0$ . We prove that, for…

math.NT2024

An almost sharp quantitative version of the Duffin-Schaeffer conjecture

Dimitris Koukoulopoulos, James Maynard, Daodao Yang

We prove a quantitative version of the Duffin-Schaeffer conjecture with an almost sharp error term. Precisely, let $I ¨ : N \to [0, 1/2]$ be a function such that the series $\su…

math.NT2024

A lower bound on the mean value of the ErdÅs-Hooley Delta function

Kevin Ford, Dimitris Koukoulopoulos, Terence Tao

We give an improved lower bound for the average of the ErdÅs-Hooley function $I^ (n)$ , namely $\sum_{n \leq x} I^ (n) ≫_{ε} x (lo g lo g x)^{1 + I^\cdot - ε}$ for all $x\geqs…

A logarithmic structure theorem for multiplicative functions with small partial sums

Irreducibility and Galois groups of random reciprocal polynomials of large degree

On Arratia's coupling and the Dirichlet law for the factors of a random integer

ErdÅs's integer dilation approximation problem and GCD graphs

An almost sharp quantitative version of the Duffin-Schaeffer conjecture

A lower bound on the mean value of the ErdÅs-Hooley Delta function

ErdÅs's integer dilation approximation problem and GCD graphs

A lower bound on the mean value of the ErdÅs-Hooley Delta function