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19932026
most citedInferring population history with DIYABC: a user-friendly approach to Approximate Bayesian Computation

688 citations

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math.NT2025

Revisiting the Fermat-type equation

Nicolas Billerey, Imin Chen, Lassina Dembélé +2

We solve the Fermat-type equation \[ x^{13} + y^{13} = 3 z^7, \qquad \gcd(x,y,z) = 1 \] combining a unit sieve, the multi-Frey modular method, level raising, computations of system…

math.NT2025

A Normality Conjecture on Rational Base Number Systems

Mélodie Andrieu, Shalom Eliahou, Léo Vivion

The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two…

math.NT2025

On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line

Sebastien Darses, Berend Ringeling, Emmanuel Royer

We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were…

math.NT2025

Low-lying zeros in families of Maass form L-functions: an extended density theorem

Martin Čech, Lucile Devin, Daniel Fiorilli +2

We study the one-level density of low-lying zeros in the family of Maass form -functions of prime level tending to infinity. Generalizing the influential work of Iwaniec, Lu…

math.NT2025

The number system in rational base and the problem

Shalom Eliahou, Jean-Louis Verger-Gaugry

The representation of numbers in rational base was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case . Unnoticed since then, nat…

math.NT2025

Effective Darmon's program for the generalised Fermat equation

Martin Azon

We follow the ideas of Darmon's program for solving infinite families of generalised Fermat equations of signatures and , where, is a fixed prime and is…