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{{ Infobox scientist
| name              = Giuseppe Melfi
| image             = Melfi2004.jpg
| image_size        = 
| caption           = 
| birth_date        = {{birth date and age|1967|06|11|df=y}}
| birth_place       = [[Uznach]], [[Switzerland]]
| death_date        = 
| death_place       = 
| nationality       = {{flag|Italy}} <br> {{flag|Switzerland}}
| fields            = [[Mathematics]]
| workplaces        = [[University of Neuchâtel]]<br>[[University of Applied Sciences Western Switzerland]]<br>University of Teacher Education BEJUNE
| alma_mater        = 
| doctoral_advisor  = 
| doctoral_students = 
| known_for         = [[Practical number]]s<br>[[Eisenstein series|Ramanujan-type identities]]
| awards            = Premio Ulisse (2010)
}}
'''Giuseppe Melfi''' (born June 11, 1967) is an [[Italy|Italo]]-[[Switzerland|Swiss]] [[mathematician]]. He achieved his [[PhD]] in mathematics in 1997 at the [[University of Pisa]]. 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 work==
His major contributions are in the theory of [[practical number]]s. This prime-like sequence of numbers is known for having an asymptotic behavior and other distribution properties similar to the sequence of [[Prime number|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 <math>m-2,m,m+2</math>.

Another notable contribution has been in an application of the theory of [[modular forms]], where he found new [[Eisenstein series|Ramanujan-type identities]] for the [[divisor function|sum-of-divisor functions]]. In particular he found the remarkable identity
:<math> \sum_{k=0}^n\sigma_1(3k+1)\sigma_1(3n-3k+1)=\frac19\sigma_3(3n+2),</math>
where <math>\sigma_k(n)</math> is the sum of the <math>k</math>-th powers of divisors of <math>n</math>.

Other topics of research include [[sum-free sequence]]s in a joint work with [[Paul Erdős|Erdős]] and [[Jean-Marc Deshouillers|Deshouillers]] and other problems in elementary [[number theory]].

In applied mathematics his research interests include [[probability]] and [[simulation]].

== Selected research publications ==

*{{cite book|author=Giuseppe Melfi and Yadolah Dodge|title=Premiers pas en simulation|publisher=[[Springer Science+Business Media|Springer-Verlag]]|year=2008|isbn=978-2-287-79493-3}}

== See also ==
* [[Applications of randomness]]

== External links ==
* [http://www2.unine.ch/Jahia/site/iene/cache/offonce/pid/20830 Giuseppe Melfi's home page]
* [http://www.zentralblatt-math.org/zmath/en/search/?q=an:0848.11002&format=complete The proof of conjectures on practical numbers] and [http://www.zentralblatt-math.org/zmath/en/search/?q=an:0958.11023&format=complete the joint work with Paul Erdős] on [[Zentralblatt MATH|Zentralblatt]].
*[http://www.dm.unipi.it/gauss-pages/melfi/public_html/pratica.html Tables of practical numbers] compiled by Giuseppe Melfi
*[http://academic.research.microsoft.com/Search?query=%22Giuseppe%20Melfi%22 Academic research query for "Giuseppe Melfi"]
{{Authority control|VIAF=80538113}}

{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Melfi, Giuseppe
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Italian mathematician
| DATE OF BIRTH     = June 11, 1967
| PLACE OF BIRTH    = [[Uznach]], [[Switzerland]]
| DATE OF DEATH     =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Melfi, Giuseppe}}
[[Category:1967 births]]
[[Category:20th-century Italian mathematicians]]
[[Category:21st-century Italian mathematicians]]
[[Category:Living people]]
[[Category:Number theorists]]
[[Category:Sicilian mathematicians]]
[[Category:University of Neuchâtel faculty]]