'E. Delaygue

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math.NT2026

On Ruzsa's conjecture on congruence preserving functions

Ã. Delaygue

Ruzsa's conjecture asserts that any sequence $(a_{n})_{n \geq 0}$ of integers that preserves congruences, $i.e.$ , satisfies $a_{n + k} \equiv a_{n} mod k$ , and has the growth…

math.NT2025

Abel's problem, Gauss and Cartier congruences over number fields

Ãric Delaygue, Tanguy Rivoal

Abel's problem consists in identifying the conditions under which the diferential equation $y^{'} = I^\cdot y$ , with $I^\cdot$ an algebraic function in $C (x)$ , possesses a non-zero algebr…