A. Languasco

activity

20072024

most citedThe number of Goldbach representations of an integer

26 citations · 268 across the 41 of their papers we have counts for

collaborators

44 papers

math.NT2024

Relative class numbers and Euler-Kronecker constants of maximal real cyclotomic subfields

Neelam Kandhil, Alessandro Languasco, Pieter Moree +2

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 $ζ_{K} (s)$ at $s = 1$ . We study the…

math.NT2024★ 1 cited

Euler constants from primes in arithmetic progression

Alessandro Languasco, Pieter Moree

Many Dirichlet series of number theoretic interest can be written as a product of generating series $ζ_{d, a} (s) = p \equiv a (mod d) \prod (1 - p^{- s})^{- 1}$ , with $p$ ranging…

math.NT2024★ 2 cited

The Kummer ratio of the relative class number for prime cyclotomic fields

Neelam Kandhil, Alessandro Languasco, Pieter Moree +2

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…

math.NT2024

The Brauer-Siegel ratio for prime cyclotomic fields

Neelam Kandhil, Alessandro Languasco, Pieter Moree

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 cyc…

math.NT2023

Sequences of integers generated by two fixed primes

Alessandro Languasco, Florian Luca, Pieter Moree +1

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 $a, b \geq 0$ . Tijdeman gave a lower bou…

math.NT2023★ 2 cited

Numerical estimates on the Landau-Siegel zero and other related quantities

Alessandro Languasco

Let $q$ be a prime, $χ$ be a non-principal Dirichlet character $mod q$ and $L (s, χ)$ be the associated Dirichlet $L$ -function. For every odd prime $q \leq 1 0^{7}$ , we show that $L(1,…

math.NT2021★ 3 cited

A unified strategy to compute some special functions of number-theoretic interest

Alessandro Languasco

We introduce an algorithm to compute the functions belonging to a suitable set $F$ defined as follows: $f \in F$ means that $f (s, x)$ , $s\in A\subset {\mathbb R…

math.NT2021★ 8 cited

Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms

Alexandru Ciolan, Alessandro Languasco, Pieter Moree

In 1961, Rankin determined the asymptotic behavior of the number $S_{k, q} (x)$ of positive integers $n \leq x$ for which a given prime $q$ does not divide $σ_{k} (n),$ the $k$ -th divisor…

math.NT2020★ 9 cited

Uniform effective estimates for $∣ L (1, χ) ∣$

Alessandro Languasco, Timothy S. Trudgian

Let $L (s, χ)$ be the Dirichlet $L$ -function associated to a non-principal primitive Dirichlet character $χ$ defined modulo $q$ , where $q \geq 3$ . We prove, under the assumption of the…

math.NT2020★ 6 cited

Numerical verification of Littlewood's bounds for $∣ L (1, χ) ∣$

Alessandro Languasco

Let $L (s, χ)$ be the Dirichlet $L$ -function associated to a non trivial primitive Dirichlet character $χ$ defined $mod q$ , where $q$ is an odd prime. In this paper we introduce a…

math.NT2020

Small values of $∣ L^{'} / L (1, χ) ∣$

Youness Lamzouri, Alessandro Languasco

In this paper, we investigate the quantity $m_{q} := min_{χ \neq = χ_{0}} ∣ L^{'} / L (1, χ) ∣$ , as $q \to \infty$ over the primes, where $L (s, χ)$ is the Dirichlet $L$ -function attached to a n…

math.NT2020★ 15 cited

A fast algorithm to compute the Ramanujan-Deninger gamma-function and some number-theoretic applications

Alessandro Languasco, Luca Righi

We introduce a fast algorithm to compute the Ramanujan-Deninger gamma function and its logarithmic derivative at positive values. Such an algorithm allows us to greatly extend the…

math.NT2019★ 2 cited

Computation of the Kummer ratio of the class number for prime cyclotomic fields

Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin +1

Let $ζ_{q}$ be a primitive $q^{th}$ root of unity with $q$ an arbitrary odd prime. The ratio of Kummer's first factor of the class number of the cyclotomic number field $\math…

math.NT2019★ 12 cited

Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields

Alessandro Languasco

We introduce a new algorithm, which is faster and requires less computing resources than the ones previously known, to compute the Euler-Kronecker constants $G_{q}$ for th…

math.NT2018★ 2 cited

Short intervals asymptotic formulae for binary problems with prime powers, II

Alessandro Languasco, Alessandro Zaccagnini

We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n = p_{1}^{ℓ_{1}} + p_{2}^{ℓ_{2}}$ and $n…

math.NT2018

On an average ternary problem with prime powers

Marco Cantarini, Alessandro Gambini, Alessandro Languasco +1

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

math.NT2018★ 5 cited

Short intervals asymptotic formulae for binary problems with prime powers

Alessandro Languasco, Alessandro Zaccagnini

We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n = p_{1}^{ℓ_{1}} + p_{2}^{ℓ_{2}}$ , with $\ell_1…

math.NT2018★ 2 cited

A Cesàro average for an additive problem with prime powers

Alessandro Languasco, Alessandro Zaccagnini

In this paper we extend and improve our results on weighted averages for the number of representations of an integer as a sum of two powers of primes. Let $1 \leq ℓ_{1} \leq ℓ_{2}$ …

math.NT2018

Sums of one prime power and two squares of primes in short intervals

Alessandro Languasco, Alessandro Zaccagnini

Let $k \geq 1$ be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers $n = p_{1}^{k} + p_{2}^{2} + p_{3}^{2}$ , where $p_{1}, p_{2}, p_{3}$ …

math.NT2018

On the Waring-Goldbach problem on average

Alessandro Languasco

Let $s$ , $ℓ$ be two integers such that $2 \leq s \leq ℓ - 1$ , $ℓ \geq 3$ . We prove that a suitable asymptotic formula for the average number of representations of integers $n=\sum…

math.NT2018★ 3 cited

A Cesàro Average of generalised Hardy-Littlewood numbers

Alessandro Languasco, Alessandro Zaccagnini

We continue our recent work on additive problems with prime summands: we already studied the \emph{average} number of representations of an integer as a sum of two primes, and also…

math.NT2017

A Diophantine approximation problem with two primes and one $k$ -th power of a prime

Alessandro Gambini, Alessandro Languasco, Alessandro Zaccagnini

We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a $k$ -th power of a prime which was only proved to hold for $1 < k < 4/3$ .…

math.NT2017★ 6 cited

Sums of four prime cubes in short intervals

Alessandro Languasco, Alessandro Zaccagnini

We prove that a suitable asymptotic formula for the average number of representations of integers $n = p_{1}^{3} + p_{2}^{3} + p_{3}^{3} + p_{4}^{3}$ , where $p_{1}, p_{2}, p_{3}, p_{4}$ are prime num…

math.NT2016★ 5 cited

Applications of some exponential sums on prime powers: a survey

Alessandro Languasco

A survey paper on some recent results on additive problems with prime powers.

Relative class numbers and Euler-Kronecker constants of maximal real cyclotomic subfields

Euler constants from primes in arithmetic progression

The Kummer ratio of the relative class number for prime cyclotomic fields

The Brauer-Siegel ratio for prime cyclotomic fields

Sequences of integers generated by two fixed primes

Numerical estimates on the Landau-Siegel zero and other related quantities

A unified strategy to compute some special functions of number-theoretic interest

Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms

Uniform effective estimates for ∣L(1,χ)∣

Numerical verification of Littlewood's bounds for ∣L(1,χ)∣

Small values of ∣L′/L(1,χ)∣

A fast algorithm to compute the Ramanujan-Deninger gamma-function and some number-theoretic applications

Computation of the Kummer ratio of the class number for prime cyclotomic fields

Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields

Short intervals asymptotic formulae for binary problems with prime powers, II

On an average ternary problem with prime powers

Short intervals asymptotic formulae for binary problems with prime powers

A Cesàro average for an additive problem with prime powers

Sums of one prime power and two squares of primes in short intervals

On the Waring-Goldbach problem on average

A Cesàro Average of generalised Hardy-Littlewood numbers

A Diophantine approximation problem with two primes and one k-th power of a prime

Sums of four prime cubes in short intervals

Applications of some exponential sums on prime powers: a survey

Uniform effective estimates for $∣ L (1, χ) ∣$

Numerical verification of Littlewood's bounds for $∣ L (1, χ) ∣$

Small values of $∣ L^{'} / L (1, χ) ∣$

A Diophantine approximation problem with two primes and one $k$ -th power of a prime