Maksym Radziwill

activity

20112026

most citedA note on the Liouville function in short intervals

18 citations · 31 across the 13 of their papers we have counts for

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Showing 2018Show all

5 papers · 1 filter

math.NT2018

Fourier uniformity of bounded multiplicative functions in short intervals on average

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Let $λ$ denote the Liouville function. We show that as $X \to \infty$ , $\int_{X}^{2 X} α sup x < n \leq x + H \sum λ (n) e (- α n) d x = o (X H)$ for all…

math.NT2018

Another application of Linnik's dispersion method

Étienne Fouvry, Maksym Radziwiłł

Let $α_{m}$ and $β_{n}$ be two sequences of real numbers supported on $[M, 2 M]$ and $[N, 2 N]$ with $M = X^{1/2 - δ}$ and $N = X^{1/2 + δ}$ . We show that there exists a $δ_{0} > 0$ such t…

math.NT2018

Level of distribution of unbalanced convolutions

Étienne Fouvry, Maksym Radziwiłł

We show that if an essentially arbitrary sequence supported on an interval containing $x$ integers, is convolved with a tiny Siegel-Walfisz-type sequence supported on an interval c…

math.NT2018

A note on the dimension of the largest simple Hecke submodule

Sandro Bettin, Corentin Perret-Gentil, Maksym Radziwiłł

For $k \geq 2$ even, let $d_{k, N}$ denote the dimension of the largest simple Hecke submodule of $S_{k} (Γ_{0} (N); Q)^{new}$ . We show, using a simple analytic method, that…

math.NT2018

Triple correlation and long gaps in the spectrum of flat tori

Christoph Aistleitner, Valentin Blomer, Maksym Radziwiłł

We evaluate the triple correlation of eigenvalues of the Laplacian on generic flat tori in an averaged sense. As two consequence we show that (a) the limit inferior (resp. limit su…