Kaisa Matomäki

activity

20122024

most citedAn averaged form of Chowla's conjecture

132 citations · 277 across the 17 of their papers we have counts for

collaborators

21 papers

math.NT2024

Weighted sieves with switching

Kaisa Matomäki, Sebastian Zuniga Alterman

Weighted sieves are used to detect numbers with at most $S$ prime factors with $S \in N$ as small as possible. When one studies problems with two variables in somewhat sym…

math.NT2023

The eighth moment of Dirichlet L-functions II

Vorrapan Chandee, Xiannan Li, Kaisa Matomäki +1

We prove an asymptotic formula for the eighth moment of Dirichlet $L$ -functions averaged over primitive characters $χ$ modulo $q$ , over all moduli $q \leq Q$ and with a short averag…

math.NT2023★ 1 cited

A note on exceptional characters and non-vanishing of Dirichlet $L$ -functions

Martin Čech, Kaisa Matomäki

We study non-vanishing of Dirichlet $L$ -functions at the central point under the unlikely assumption that there exists an exceptional Dirichlet character. In particular we prove th…

math.NT2023

Products of primes in arithmetic progressions

Kaisa Matomäki, Joni Teräväinen

A conjecture of Erdős states that, for any large prime $q$ , every reduced residue class $(mod q)$ can be represented as a product $p_{1} p_{2}$ of two primes $p_{1}, p_{2} \leq q$ . We establi…

math.NT2022★ 10 cited

Higher uniformity of arithmetic functions in short intervals I. All intervals

Kaisa Matomäki, Xuancheng Shao, Terence Tao +1

We study higher uniformity properties of the Möbius function $μ$ , the von Mangoldt function $Λ$ , and the divisor functions $d_{k}$ on short intervals $(X, X + H]$ with $X^{θ+\varepsilon…

cs.NE2021

Towards a Principled Learning Rate Adaptation for Natural Evolution Strategies

Masahiro Nomura, Isao Ono

Natural Evolution Strategies (NES) is a promising framework for black-box continuous optimization problems. NES optimizes the parameters of a probability distribution based on the…

math.NT2020★ 15 cited

Higher uniformity of bounded multiplicative functions in short intervals on average

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao +2

Let $λ$ denote the Liouville function. We show that, as $X \to \infty$ , $$\int_{X}^{2X} \sup_{\substack{P(Y)\in \mathbb{R}[Y]\\ deg(P)\leq k}} \Big | \sum_{x \leq n \leq x…

math.NT2020★ 11 cited

On the variance of squarefree integers in short intervals and arithmetic progressions

Ofir Gorodetsky, Kaisa Matomäki, Maksym Radziwiłł +1

We evaluate asymptotically the variance of the number of squarefree integers up to $x$ in short intervals of length $H < x^{6/11 - ε}$ and the variance of the number of s…

math.NT2019★ 11 cited

On the Möbius function in all short intervals

Kaisa Matomäki, Joni Teräväinen

We show that, for the Möbius function $μ (n)$ , we have $x < n \leq x + x^{θ} \sum μ (n) = o (x^{θ})$ for any $θ > 0.55$ . This improves on a result of Ramachandra from 1976, which is valid f…

math.NT2017★ 2 cited

Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

We study the problem of obtaining asymptotic formulas for the sums $\sum_{X < n \leq 2 X} d_{k} (n) d_{l} (n + h)$ and $\sum_{X < n \leq 2 X} Λ (n) d_{k} (n + h)$ , where $Λ$ is the von Mangoldt fu…

math.NT2017★ 22 cited

Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

We show that the expected asymptotic for the sums $\sum_{X < n \leq 2 X} Λ (n) Λ (n + h)$ , $\sum_{X < n \leq 2 X} d_{k} (n) d_{l} (n + h)$ , and $\sum_{X < n \leq 2 X} Λ (n) d_{k} (n + h)$ hold for almo…

math.NT2016★ 27 cited

Vinogradov's theorem with almost equal summands

Kaisa Matomäki, James Maynard, Xuancheng Shao

Let $θ > 11/20$ . We prove that every sufficiently large odd integer $n$ can be written as a sum of three primes $n = p_{1} + p_{2} + p_{3}$ with $∣ p_{i} - n /3∣ \leq n^{θ}$ for $i \in {1, 2, 3}$ …

math.NT2015★ 22 cited

Vinogradov's three primes theorem with almost twin primes

Kaisa Matomäki, Xuancheng Shao

In this paper we prove two results concerning Vinogradov's three primes theorem with primes that can be called almost twin primes. First, for any $m$ , every sufficiently large odd…

math.NT2015★ 9 cited

Sign patterns of the Liouville and Möbius functions

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Let $λ$ and $μ$ denote the Liouville and Möbius functions respectively. Hildebrand showed that all eight possible sign patterns for $(λ (n), λ (n + 1), λ (n + 2))$ occur infinitely often.…

math.NT2015

When the sieve works II

Kaisa Matomäki, Xuancheng Shao

For a set of primes $P$ , let $Ψ (x, P)$ be the number of positive integers $n \leq x$ all of whose prime factors lie in $P$ . In this paper we classify…

math.NT2015★ 132 cited

An averaged form of Chowla's conjecture

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Let $λ$ denote the Liouville function. A well known conjecture of Chowla asserts that for any distinct natural numbers $h_{1}, \dots, h_{k}$ , one has $\sum_{1 \leq n \leq X} λ(n+h_1) \do…

math.NT2015

Multiplicative functions in short intervals

Kaisa Matomäki, Maksym Radziwiłł

We introduce a general result relating "short averages" of a multiplicative function to "long averages" which are well understood. This result has several consequences. First, for…

math.NT2015

Small scale distribution of zeros and mass of modular forms

Stephen Lester, Kaisa Matomäki, Maksym Radziwiłł

We study the behavior of zeros and mass of holomorphic Hecke cusp forms on $S L_{2} (Z) \ H$ at small scales. In particular, we examine the distribution of the…

math.NT2014★ 5 cited

Sign changes of Hecke eigenvalues

Kaisa Matomäki, Maksym Radziwill

Let $f$ be a holomorphic or Maass Hecke cusp form for the full modular group and write $λ_{f} (n)$ for the corresponding Hecke eigenvalues. We are interested in the signs of those eig…

math.NT2012★ 10 cited

When the sieve works

Andrew Granville, Dimitris Koukoulopoulos, Kaisa Matomäki

We are interested in classifying those sets of primes $P$ such that when we sieve out the integers up to $x$ by the primes in $P^{c}$ we are left with roughly the…

cs.DM2012

A new geometric approach to Sturmian words

Kaisa Matomäki, Kalle Saari

We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using…

Weighted sieves with switching

The eighth moment of Dirichlet L-functions II

A note on exceptional characters and non-vanishing of Dirichlet L-functions

Products of primes in arithmetic progressions

Higher uniformity of arithmetic functions in short intervals I. All intervals

Towards a Principled Learning Rate Adaptation for Natural Evolution Strategies

Higher uniformity of bounded multiplicative functions in short intervals on average

On the variance of squarefree integers in short intervals and arithmetic progressions

On the Möbius function in all short intervals

Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges

Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

Vinogradov's theorem with almost equal summands

Vinogradov's three primes theorem with almost twin primes

Sign patterns of the Liouville and Möbius functions

When the sieve works II

An averaged form of Chowla's conjecture

Multiplicative functions in short intervals

Small scale distribution of zeros and mass of modular forms

Sign changes of Hecke eigenvalues

When the sieve works

A new geometric approach to Sturmian words

A note on exceptional characters and non-vanishing of Dirichlet $L$ -functions