Maksym Radziwill

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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 RadziwiÅÅ

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.NT2026

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

Kaisa MatomÃ¤ki, Maksym RadziwiÅÅ, Xuancheng Shao +2

We study higher uniformity properties of the von Mangoldt function $I^$ , the MÃ¶bius function $I^¼$ , and the divisor functions $d_{k}$ on short intervals $(x, x + H]$ for almost all $x \…

math.NT2025

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

Mayank Pandey, Maksym RadziwiÅÅ

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^{2Ïi n Î±} \Big | d Î±…

math.NT2025

Gap distribution of $n mod 1$ and the circle method

Maksym RadziwiÅÅ, Niclas Technau

The distribution of the properly renormalized gaps of $n mod 1$ with $n < N$ converges (when $N \to \infty$ ) to a non-standard limit distribution, as Elk…

Exponential sums over primes

Sign changes of the Liouville function in arithmetic progressions

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

L1 means of exponential sums with multiplicative coefficients. II

Gap distribution of n​mod1 and the circle method

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

Gap distribution of $n mod 1$ and the circle method