Zobrazeno 1 - 10
of 514
pro vyhledávání: '"Languasco, A."'
Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet $L$-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude
Externí odkaz:
http://arxiv.org/abs/2411.19762
The Euler--Kronecker constant of a number field $K$ is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_K(s)$ at $s=1$. We study the distribution of the Euler--Kronecker constant $\gamma_q^+$ of the
Externí odkaz:
http://arxiv.org/abs/2407.09113
Autor:
Languasco, Alessandro, Moree, Pieter
Publikováno v:
Math. Comp. 2025
Many Dirichlet series of number theoretic interest can be written as a product of generating series $\zeta_{\,d,a}(s)=\prod\limits_{p\equiv a\pmod{d}}(1-p^{-s})^{-1}$, with $p$ ranging over all the primes in the primitive residue class modulo $a\pmod
Externí odkaz:
http://arxiv.org/abs/2406.16547
The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a Siegel zero o
Externí odkaz:
http://arxiv.org/abs/2402.13830
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Ri
Externí odkaz:
http://arxiv.org/abs/2402.13829
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutive integers of the form $p^a\cdot q^b$ with $a,b\ge 0$. Tijdeman gave a lower bound (1973) and an upper bound (1974) for the gap size $n_{i+1}-n_i$, wi
Externí odkaz:
http://arxiv.org/abs/2309.12806
Autor:
Languasco, Alessandro
Let $q$ be a prime, $\chi$ be a non-principal Dirichlet character $\bmod\ q$ and $L(s,\chi)$ be the associated Dirichlet $L$-function. For every odd prime $q\le 10^7$, we show that $L(1,\chi_\square) > c_{1} \log q$ and $\beta < 1- \frac{c_{2}}{\log
Externí odkaz:
http://arxiv.org/abs/2301.10722
Autor:
Giorgia Fedele, Josep Armengol, Tito Caffi, Luca Languasco, Nedeljko Latinovic, Jelena Latinovic, Maela León, Guido Marchi, Laura Mugnai, Vittorio Rossi
Publikováno v:
Frontiers in Plant Science, Vol 15 (2024)
Phomopsis cane and leaf spot (PCLS) disease, affecting grapevines (Vitis vinifera and Vitis spp.), has been historically associated with Diaporthe ampelina. Typical disease symptoms, comprising bleaching and black pycnidia, have also been associated
Externí odkaz:
https://doaj.org/article/67d09763374f48568fabbd438cc2baaf
Autor:
Languasco, Alessandro
Publikováno v:
J. Number Theory, 247 (2023), 118--161
We introduce an algorithm to compute the functions belonging to a suitable set ${\mathscr F}$ defined as follows: $f\in {\mathscr F}$ means that $f(s,x)$, $s\in A\subset {\mathbb R}$ being fixed and $x>0$, has a power series expansion centred at $x_0
Externí odkaz:
http://arxiv.org/abs/2111.07686
Publikováno v:
Journal of Mathematical Analysis and Applications, 2022
In 1961, Rankin determined the asymptotic behavior of the number $S_{k,q}(x)$ of positive integers $n\le x$ for which a given prime $q$ does not divide $\sigma_k(n),$ the $k$-th divisor sum function. By computing the associated Euler-Kronecker consta
Externí odkaz:
http://arxiv.org/abs/2109.03288