6 citations · 16 across the 13 of their papers we have counts for
13 papers
Cyclotomy of symmetric polynomials
Laura De Carli, Maurizio Laporta
We prove some new identities for homogeneous symmetric polynomials when evaluated at roots of unity. Some of these formulas are applied to obtain new insights onto cyclotomic polyn…
Divisibility criteria and coefficient formulas for cyclotomic polynomials
Laura De Carli, Maurizio Laporta
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of…
Approximating the divisor functions
Andrew Echezabal, Laura De Carli, Maurizio Laporta
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof…
On Ramanujan expansions and primes in arithmetic progressions
Maurizio Laporta
A celebrated theorem of Delange gives a sufficient condition for an arithmetic function to be the sum of the associated Ramanujan expansion with the coefficients provided by a prev…
The Hardy-Littlewood conjectures on the twin primes and the binary Goldbach problem are true
Maurizio Laporta
A celebrated conjecture of Hardy and Littlewood provides with an asymptotic formula for the counting function of the twin primes. We give an unconditional proof of such a formula b…
Sieve functions in arithmetic bands, II
Giovanni Coppola, Maurizio Laporta
An arithmetic function is called a of if its Eratosthenes transform has support in , where $g(q)\ll_{\varepsilon} q^{\varepsilo…