Výsledky vyhledávání - "Bellotti, Chiara"

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An explicit log-free zero density estimate for the Riemann zeta-function

Autor: Bellotti, Chiara

We will provide an explicit log-free zero-density estimate for $\zeta(s)$ of the form $N(\sigma,T)\le AT^{B(1-\sigma)}$. In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for $\sigma\in[\alpha_0,1]$, wit

Externí odkaz: http://arxiv.org/abs/2405.12545

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Explicit zero density estimate near unity

Autor: Bellotti, Chiara

We will provide the first explicit zero-density estimate for $\zeta$ of the form $N(\sigma,T)\le \mathcal{C}T^{B(1-\sigma)^{3/2}}(\log T)^C$. In particular, we improve $C$ to $10393/900=11.547\dots.$
Comment: 24 pages

Externí odkaz: http://arxiv.org/abs/2311.05136

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Explicit bounds for the Riemann zeta function and a new zero-free region

Autor: Bellotti, Chiara

We prove that $|\zeta(\sigma+it)|\le 70.7 |t|^{4.438 (1-\sigma)^{3/2}}\log^{2/3}|t|$ for $1/2\le\sigma\le 1$ and $|t|\ge 3$. As a consequence, we improve the explicit zero-free region for $\zeta(s)$, showing that $\zeta(\sigma+it)$ has no zeros in th

Externí odkaz: http://arxiv.org/abs/2306.10680

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On the generalised Dirichlet divisor problem

Autor: Bellotti, Chiara, Yang, Andrew

We improve unconditional estimates on $\Delta_k(x)$, the remainder term of the generalised divisor function, for large $k$. In particular, we show that $\Delta_k(x) \ll x^{1 - 1.889k^{-2/3}}$ for all sufficiently large fixed $k$.
Comment: 17 pag

Externí odkaz: http://arxiv.org/abs/2303.05028

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A conditional result on exponential sums over primes in short intervals

Autor: Bellotti, Chiara, Puglisi, Giuseppe

The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet $L$-functions are true

Externí odkaz: http://arxiv.org/abs/2211.15546

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New bounds for numbers of primes in element orders of finite groups

Autor: Bellotti, Chiara, Keller, Thomas Michael, Trudgian, Timothy S.

Let $\rho(n)$ denote the maximal number of different primes that may occur in the order of a finite solvable group $G$, all elements of which have orders divisible by at most $n$ distinct primes. We show that $\rho(n)\leq 5n$ for all $n\geq 1$. As an

Externí odkaz: http://arxiv.org/abs/2211.05837

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Elementary methods in the study of Deuring-Heilbronn Phenomenon

Autor: Bellotti, Chiara, Puglisi, Giuseppe

The aim of this work is to improve some elementary results regarding both the Deuring-Phenomenon and the Heilbronn-Phenomenon. We will give better estimates regarding both the influence of zeros of the Riemann zeta function on the exceptional zeros a

Externí odkaz: http://arxiv.org/abs/2201.03990

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