Degree cum laude, University Pisa, 1993. Doctor of Philosophy in Mathematics, University Pisa, 1997.
After some years spent at the University of Lausanne, he works now at the University of Neuchâtel, as well as at the University of Applied Sciences Western Switzerland and at the local University of Teacher Education. His major contributions are in the theory of practical numbers. This prime-like sequence of numbers is known for having an asymptotic behavior and other distribution properties similar to the sequence of primes.
Melfi proved two conjectures both raised in 1984 one of which is the corresponding of the Goldbach conjecture for practical numbers: every even number is a sum of two practical numbers. He also proved that there exist infinitely many triples of practical numbers of the form. Another notable contribution has been in an application of the theory of modular forms, where he found new Ramanujan-type identities for the sum-of-divisor functions.
In particular he found the remarkable identity where is the sum of the -th powers of divisors of. In a joint work with Erdős and Deshouillers he proved the existence of sum-free sequences having a polynomial growing: so he has an Erdős number = 1 being one of the 511 direct collaborators to the Hungarian mathematician disappeared in 1996. Among other problems in elementary number theory, he is the author of a theorem that allowed him getting a 5328-digit number that is at present the largest known primitive weird number.
In applied mathematics his research interests include probability and simulation.
Member of Swiss Statistical Society, Swiss Mathematics Society.
Married Margarita Smirnova, December 24, 2004.