Luca Ghidelli

activity

20192022

most citedMultiplicative Ramanujan coefficients of null-function

1 citations · 3 across the 7 of their papers we have counts for

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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

On gaps between sums of four fourth powers

Luca Ghidelli

We prove that for almost all $N$ there is a sum of four fourth powers in the interval $(N - N^{γ}, N]$ , for all $γ > 4059/16384 = 0.24774..$ .

math.NT2019★ 1 cited

Arithmetic properties of cubic and biquadratic theta series

Luca Ghidelli

A cubic (resp. biquadratic) theta series is a power series whose n-th coefficient is equal to 1 if n is a perfect cube (resp. fourth power) and zero otherwise. We improve on a resu…

math.NT2019

Arbitrarily long gaps between the values of positive-definite cubic and biquadratic diagonal forms

Luca Ghidelli

For $s = 3, 4$ , we prove the existence of arbitrarily long sequences of consecutive integers none of which is a sum of $s$ nonnegative $s$ -th powers. More generally, we study the exis…