Maksym Radziwill

activity

20092026

most citedAn averaged form of Chowla's conjecture

132 citations · 469 across the 54 of their papers we have counts for

collaborators

67 papers

math.CA2026

Uniformly Bounded Orthonormal Bases of Homogeneous Polynomials on the Complex Sphere

Felipe Gonçalves, João P. Ferreira, Maksym Radziwiłł

We resolve the long-standing problem of Rudin concerning uniformly bounded orthonormal bases of homogeneous polynomials on complex unit spheres. Specifically, we show that for ever…

math.NT2026

Exponential sums over primes

James Maynard, Mayank Pandey, Maksym Radziwiłł

Let $α = a / q + ε$ with $(a, q) = 1$ , $q \leq N^{1/2}$ and $∣ ε ∣ \leq 1/ (q N^{1/2})$ , and let $B := max (q, q N ∣ ε ∣)$ . We show that \[ \Bigl|\sum_{n<N}Λ(n)e(nα)\Bigr|\le N^{o(1)}\Bigl(\frac{N}{B^{1/2…

math.NT2026

Sign changes of the Liouville function in arithmetic progressions

Kevin Ford, Maksym Radziwiłł

We show that for any $ε > 0$ , prime $q$ sufficiently large with respect to $1/ ε$ and residue class $(a, q) = 1$ , there exist two integers $m, n \leq q^{5/2 + \…

math.DS2025

Density of orbits of horocycle flows at sub-quadratic polynomial times

Adam Kanigowski, Maksym Radziwiłł

Let $Γ \subset P S L (2, R)$ be such that the space $X = Γ\ P S L (2, R)$ is not compact. Let $(h_{t})$ be the horocycle flow acting on $X$ . We show that for every $x…

math.NT2025

$L^{1}$ means of exponential sums with multiplicative coefficients. II

Mayank Pandey, Maksym Radziwiłł

Let $f$ be a real-valued $1$ -bounded multiplicative function. Suppose that the mean-value of $f^{2}$ exists, and $$\int_{0}^{1} \Big | \sum_{n \leq N} f(n)e^{2πi n α} \Big | d α\le…

math.NT2024

Higher uniformity of arithmetic functions in short intervals II. Almost all intervals

Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2

We study higher uniformity properties of the von Mangoldt function $Λ$ , the Möbius function $μ$ , and the divisor functions $d_{k}$ on short intervals $(x, x + H]$ for almost all $x \in…