Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Matomäki, Kaisa"'
We study higher uniformity properties of the von Mangoldt function $\Lambda$, the M\"obius function $\mu$, and the divisor functions $d_k$ on short intervals $(x,x+H]$ for almost all $x \in [X, 2X]$. Let $\Lambda^\sharp$ and $d_k^\sharp$ be suitable
Externí odkaz:
http://arxiv.org/abs/2411.05770
In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $\chi$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large
Externí odkaz:
http://arxiv.org/abs/2409.01457
Weighted sieves are used to detect numbers with at most $S$ prime factors with $S \in \mathbb{N}$ as small as possible. When one studies problems with two variables in somewhat symmetric roles (such as Chen primes, that is primes $p$ such that $p+2$
Externí odkaz:
http://arxiv.org/abs/2405.19063
Autor:
Matomäki, Kaisa, Teräväinen, Joni
In this note we investigate connections between zero density estimates for the Riemann zeta function and large value estimates for Dirichlet polynomials. It is well known that estimates of the latter type imply estimates of the former type. Our goal
Externí odkaz:
http://arxiv.org/abs/2403.13157
We develop a sieve that can detect primes in multiplicatively structured sets under certain conditions. We apply it to obtain a new $L$-function free proof of Linnik's problem of bounding the least prime $p$ such that $p\equiv a\pmod q$ (with the bou
Externí odkaz:
http://arxiv.org/abs/2401.17570
We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was shown condit
Externí odkaz:
http://arxiv.org/abs/2307.13194
Autor:
Čech, Martin, Matomäki, Kaisa
Publikováno v:
Math. Ann. (2023)
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 that if $\psi$ is a real primitive character modulo $D \in \mathbb{N}$ w
Externí odkaz:
http://arxiv.org/abs/2303.05277
Autor:
Matomäki, Kaisa, Teräväinen, Joni
A conjecture of Erd\H{o}s states that, for any large prime $q$, every reduced residue class $\pmod q$ can be represented as a product $p_1p_2$ of two primes $p_1,p_2\leq q$. We establish a ternary version of this conjecture, showing that, for any suf
Externí odkaz:
http://arxiv.org/abs/2301.07679
Autor:
Matomäki, Kaisa, Teräväinen, Joni
Publikováno v:
Trans. Amer. Math. Soc. 376, 5433-5459, 2023
We show that, for almost all $x$, the interval $(x, x+(\log x)^{2.1}]$ contains products of exactly two primes. This improves on a work of the second author that had $3.51$ in place of $2.1$. To obtain this improvement, we prove a new type II estimat
Externí odkaz:
http://arxiv.org/abs/2207.05038
Publikováno v:
Forum of Mathematics, Pi, 11 (2023), e29
We study higher uniformity properties of the M\"obius function $\mu$, the von Mangoldt function $\Lambda$, and the divisor functions $d_k$ on short intervals $(X,X+H]$ with $X^{\theta+\varepsilon} \leq H \leq X^{1-\varepsilon}$ for a fixed constant $
Externí odkaz:
http://arxiv.org/abs/2204.03754