Institut Élie Cartan de Lorraine

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19982026

most citedComputational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations

398 citations

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math.NT2025

How often is $x \mapsto x^{3}$ one-to-one in $Z / n Z$ ?

Olivier Garet

We characterize the integers n such that $x \mapsto x^{3}$ describes a bijection from the set $Z / n Z$ to itself and we determine the frequency of these integers. Prec…

math.NT2025

The level of distribution of the sum-of-digits function in arithmetic progressions

Nathan Toumi

For $q \geq 2$ , $n \in N$ , let $s_{q} (n)$ denote the sum of the digits of $n$ written in base $q$ . Spiegelhofer (2020) proved that the Thue--Morse sequence has level of di…

math.NT2025

Almost primes and primes that are sums of two squares plus 1

Kunjakanan Nath, Likun Xie

In this paper, we obtain a lower bound for the number of primes $p \leq x$ such that $p - 1$ is a sum of two squares and $p + 2$ has a bounded number of prime factors. The proof uses th…

How often is x↦x3 one-to-one in Z/nZ?

The level of distribution of the sum-of-digits function in arithmetic progressions

Almost primes and primes that are sums of two squares plus 1

How often is $x \mapsto x^{3}$ one-to-one in $Z / n Z$ ?