I focus my research into various areas of mathematics:

Analytic number theory: additive problems with primes and powers of primes; distribution of non-trivial zeros of Riemann Zeta function and L- functions; diophantine equations.

Special functions and symbolic calculus: closed form of particular classes of hypergoemtric functions (in particular, series whose addends are central binomial coefficients and harmonic numbers) via Fourier-Legendre expansions, integral transforms, fractional operators and combinatorial identities.

Approximation theory: mathematical properties of genealized sampling operators and neural network operators, in particular convergence results, inverse results, saturation results and Voronovskaja type formulas.

PDE: study of travelling wave solutions for one dimensional reaction-diffusion-convexion equations of Fisher-KPP type.

Capsule Bio

I was born in Umbertide (PG) in 1987. I obtained my degree in Mathematics at University of Perugia and my PhD at University of Parma (administrative headquarter: Ferrara). Subsequently, I won the INdAM grant “Ing. Giorgio Schirillo ”and a post-doc position at University of Perugia. Since February 2020 I have a post-doc position at Marche Polytechnic University.

Main publications

M. Cantarini, On the Cesàro average of the numbers that can be written as sum of a prime and two squares of primes, Journal of Number Theory 185 (2018), 194-217.

M. Cantarini, A. Gambini, A. Zaccagnini, On the average number of representations of an integer as a sum of like prime powers, Proc. Amer. Math. Soc. 148(4) (2020), 1499–1508.

M. Cantarini, D. Costarelli, G. Vinti, A solution of the problem of inverse approximation for the sampling Kantorovich operators in case of Lipschitz functions, Dolomites Research Notes on Approximation, 13 (2020) 30-35.

M. Cantarini, D. Costarelli, G. Vinti, Asymptotic expansion for neural network operators of the Kantorovich type and high order of approximation, Mediterr. J. Math. 18, 66 (2021).

J. M. Campbell, M. Cantarini, J. D’Aurizio, Symbolic computations via Fourier-Legenre expansions and fractional operators, accepted on Integral Transforms and Special Functions.