Publications associées (55)

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
2024

Toroidal families and averages of L-functions, I

Philippe Michel

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...
Polish Acad Sciences Inst Mathematics-Impan2024

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume VV for lattices in Euclidean space which are modules over the ring of integers of a number field KK. In particular, denoting by ωKω_K the number of roots of unity in KK, we ...
arXiv2023

ALGEBRAIC TWISTS OF GL3 x GL2 L-FUNCTIONS

Philippe Michel, Yongxiao Lin

We prove that the coefficients of a GL3 x GL2 Rankin-Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL2 and of Kowalski, L ...
Baltimore2023

A decomposition of multicorrelation sequences for commuting transformations along primes

Florian Karl Richter

A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer kk and every δ>0\delta>0 there exists nn such that every subset of ${1, ...
2021

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