G. Coppola

activity

20072020

most citedFinite Ramanujan expansions and shifted convolution sums of arithmetical functions

14 citations · 70 across the 30 of their papers we have counts for

collaborators

31 papers

math.NT2020

A smooth summation of Ramanujan expansions

Giovanni Coppola

We studied Ramanujan series $\sum_{q = 1}^{\infty} G (q) c_{q} (a)$ , where $c_{q} (a)$ is the well-known Ramanujan sum and the complex numbers $G (q)$ , as $q \in$ N, are the Ramanujan coefficien…

math.NT2020

Convergence of Ramanujan expansions, I [Multiplicativity on Ramanujan clouds]

Giovanni Coppola, Luca Ghidelli

We call $R_{G} (a) := \sum_{q = 1}^{\infty} G (q) c_{q} (a)$ the 'Ramanujan series', of coefficient $G :$ N $\to$ C, where $c_{q} (a)$ is the well-known Ramanujan sum. We study the convergence of this…

math.NT2020★ 1 cited

Multiplicative Ramanujan coefficients of null-function

Giovanni Coppola, Luca Ghidelli

The null-function $0 (a) := 0$ , $\forall a \in$ N, has Ramanujan expansions: $0 (a) = \sum_{q = 1}^{\infty} (1/ q) c_{q} (a)$ (where $c_{q} (a) :=$ Ramanujan sum), given by Ramanujan, and $0(a)=\sum_…

math.NT2019★ 4 cited

Finite and infinite Euler products of Ramanujan expansions

Giovanni Coppola

All the $F :$ N $\to$ C having Ramanujan expansion $F (a) = \sum_{q = 1}^{\infty} G (q) c_{q} (a)$ (here $c_{q} (a)$ is the Ramanujan sum) pointwise converging in $a \in$ N, with $G :$ N$\righ…

math.NT2019★ 3 cited

A smooth shift approach for a Ramanujan expansion

Giovanni Coppola

All arithmetical functions $F$ satisfying Ramanujan Conjecture, i.e., $F (n) ≪_{ε} n^{ε}$ , and with $Q -$ smooth divisors, i.e., with Eratosthenes transform $F':=F…

math.NT2017★ 5 cited

A map of Ramanujan expansions

Giovanni Coppola

A map is a panorama in small scale. In this half-survey, half-research paper we give general results on Ramanujan expansions. We don't include the ocean of results from the literat…