# GDR STN

Site du GDR Structuration de la théorie des nombres

## HAL : Dernières publications

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HAL : Dernières publications

## Articles syndiqués

• ### [hal-01632280] On Veech’s proof of Sarnak’s theorem on the Möbius flow

14 novembre, par El Houcein El Abdalaoui
We present Veech's proof of Sarnak's theorem on the Möbius flow which say that there is a unique admissible measure on the Möbius flow. As a consequence, we obtain that Sarnak's conjecture is equivalent to Chowla conjecture with the help of Tao's logarithmic Theorem which assert that the (...)
• ### [hal-01634444] $R^2$ Dark Energy in the Laboratory

14 novembre, par Pierre Vanhove, Philippe Brax, Patrick Valageas
We analyse the role, on large cosmological scales and laboratory experiments, of the leading curvature squared contributions to the low energy effective action of gravity. We argue for a natural relationship $c_0\lambda^2\simeq 1$ at low-energy between the $\cal R^2$ coefficients $c_0$ of the (...)
• ### [hal-01625653] A conjecture which implies that there are infinitely many primes of the form n !+1

13 novembre, par Apoloniusz Tyszka
Let f(6)=720, and let f(n+1)=f(n)! for every integer n \geq 6. For an integer n \geq 6, let \Lambda_n denote the following statement: if a system S \subseteq x_i!=x_j: 1 \leq i < j \leq n \cup x_i \cdot x_j=x_j+1: 1 \leq i < j \leq n-1 has at most finitely many solutions in integers (...)
• ### [hal-01176039] Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals

13 novembre, par El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We show that Sarnak's conjecture on M\"obius disjointness holds in every uniquely ergodic model of a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial $P\in\R[x]$ with irrational leading coefficient and for each multiplicative function (...)
• ### [hal-01630363] Equations with powers of singular moduli

13 novembre, par Antonin Riffaut
We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli j(τ), j(τ ′) such that the numbers 1, j(τ) m and j(τ ′) n are linearly dependent over Q for some positive integers m, (...)

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