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Giuseppe Melfi

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Giuseppe Melfi
Born (1967-06-11) 11 June 1967 (age 57)
Nationality Italy
  Switzerland
Known forPractical numbers
Ramanujan-type identities
AwardsPremio Ulisse (2010)[1]
Scientific career
FieldsMathematics
InstitutionsUniversity of Neuchâtel
University of Applied Sciences Western Switzerland
University of Teacher Education BEJUNE

Giuseppe Melfi (June 11, 1967) is an Italo-Swiss mathematician who works on practical numbers and modular forms.

Career

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He gained his PhD in mathematics in 1997 at the University of Pisa. After some time spent at the University of Lausanne during 1997-2000, Melfi was appointed at the University of Neuchâtel, as well as at the University of Applied Sciences Western Switzerland and at the local University of Teacher Education.

Work

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His major contributions are in the field 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[2] 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. His seven new identities extended the ten other identities found by Ramanujan in 1913.[3] In particular he found the remarkable identity

where is the sum of the divisors of and is the sum of the third powers of the divisors of .

Among other problems in elementary number theory, he is the author of a theorem that allowed him to get a 5328-digit number that has been for a while the largest known primitive weird number.

In applied mathematics his research interests include probability and simulation.

Selected research publications

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  • Giuseppe Melfi and Yadolah Dodge (2008). Premiers pas en simulation. Springer-Verlag. ISBN 978-2-287-79493-3.
  • Deshouillers, Jean-Marc; Erdős, Pál; Melfi, Giuseppe (1999), "On a question about sum-free sequences", Discrete Mathematics, 200 (1–3): 49–54, doi:10.1016/s0012-365x(98)00322-7, MR 1692278.
  • Melfi, Giuseppe (2015). "On the conditional infiniteness of primitive weird numbers". Journal of Number Theory. 147. Elsevier: 508–514. doi:10.1016/j.jnt.2014.07.024.
  • Melfi, Giuseppe (1996), "On two conjectures about practical numbers", Journal of Number Theory, 56 (1): 205–210, doi:10.1006/jnth.1996.0012, MR 1370203

See also

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References

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  1. ^ "Consegnati i premi "Ulisse", La Sicilia, 15th August 2010, p. 38". Retrieved 2021-08-10.
  2. ^ Margenstern, M., Résultats et conjectures sur les nombres pratiques, C, R. Acad. Sci. Sér. 1 299, No. 18 (1984), 895-898.
  3. ^ Ramanujan, S., On certain arithmetical functions, Transactions of the Cambridge Philosophical Society, 22 (9), 1916, p. 159-184.
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