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

Showing 2012Show all

6 papers · 1 filter

math.NT2012

Explicit relations between primes in short intervals and exponential sums over primes

Alessandro Languasco, Alessandro Zaccagnini

Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square…

math.NT2012★ 16 cited

On a ternary Diophantine problem with mixed powers of primes

Alessandro Languasco, Alessandro Zaccagnini

Let $1 < k < 33/29$ . We prove that if $λ_{1}$ , $λ_{2}$ and $λ_{3}$ are non-zero real numbers, not all of the same sign and that $λ_{1} / λ_{2}$ is irrational and $ϖ$ is any real numbe…

math.NT2012★ 11 cited

A Cesàro Average of Hardy-Littlewood numbers

Alessandro Languasco, Alessandro Zaccagnini

Let $Λ$ be the von Mangoldt function and $r_{HL} (n) = \sum_{m_{1} + m_{2}^{2} = n} Λ (m_{1}),$ be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently…

math.NT2012★ 8 cited

A Diophantine problem with prime variables

Alessandro Languasco, Alessandro Zaccagnini

We study the distribution of the values of the form $λ_{1} p_{1} + λ_{2} p_{2} + λ_{3} p_{3}^{k}$ , where $λ_{1}$ , $λ_{2}$ and $λ_{3}$ are non-zero real number not all of the same sign, with $λ_1 / λ_2…

math.NT2012★ 17 cited

A Cesàro Average of Goldbach numbers

Alessandro Languasco, Alessandro Zaccagnini

Let $Λ$ be the von Mangoldt function and $(r_{G} (n) = \sum_{m_{1} + m_{2} = n} Λ (m_{1}) Λ (m_{2}))$ be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer. We prove t…

math.NT2012

A Diophantine problem with a prime and three squares of primes

Alessandro Languasco, Alessandro Zaccagnini

We prove that if $λ_{1}$ , $λ_{2}$ , $λ_{3}$ and $λ_{4}$ are non-zero real numbers, not all of the same sign, $λ_{1} / λ_{2}$ is irrational, and $ϖ$ is any real number then, for any $\eps >…