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| {{ Infobox scientist
| | Let me first begin by introducing myself. My name is Boyd Butts even though it is not the name on my birth certificate. Hiring is her working day job now but she's always needed her personal company. Years ago we moved to North Dakota. What I love performing is doing ceramics but I haven't made a dime with it.<br><br>Here is my web-site - std testing at home ([http://www.pinaydiaries.com/user/LConsiden you can look here]) |
| | name = Giuseppe Melfi
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| | image = Melfi2004.jpg
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| | image_size =
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| | caption =
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| | birth_date = {{birth date and age|1967|06|11|df=y}}
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| | birth_place = [[Uznach]], [[Switzerland]]
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| | death_date =
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| | death_place =
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| | nationality = {{flag|Italy}} <br> {{flag|Switzerland}}
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| | fields = [[Mathematics]]
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| | workplaces = [[University of Neuchâtel]]<br>[[University of Applied Sciences Western Switzerland]]<br>University of Teacher Education BEJUNE
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| | alma_mater =
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| | doctoral_advisor =
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| | doctoral_students =
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| | known_for = [[Practical number]]s<br>[[Eisenstein series|Ramanujan-type identities]]
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| | awards = Premio Ulisse (2010)
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| }}
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| '''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.
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| ==His work==
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| 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>.
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| 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
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| :<math> \sum_{k=0}^n\sigma_1(3k+1)\sigma_1(3n-3k+1)=\frac19\sigma_3(3n+2),</math>
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| where <math>\sigma_k(n)</math> is the sum of the <math>k</math>-th powers of divisors of <math>n</math>.
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| 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]].
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| In applied mathematics his research interests include [[probability]] and [[simulation]].
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| == Selected research publications ==
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| *{{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}}
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| == See also ==
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| * [[Applications of randomness]]
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| == External links ==
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| * [http://www2.unine.ch/Jahia/site/iene/cache/offonce/pid/20830 Giuseppe Melfi's home page]
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| * [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]].
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| *[http://www.dm.unipi.it/gauss-pages/melfi/public_html/pratica.html Tables of practical numbers] compiled by Giuseppe Melfi
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| *[http://academic.research.microsoft.com/Search?query=%22Giuseppe%20Melfi%22 Academic research query for "Giuseppe Melfi"]
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| {{Authority control|VIAF=80538113}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Melfi, Giuseppe
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Italian mathematician
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| | DATE OF BIRTH = June 11, 1967
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| | PLACE OF BIRTH = [[Uznach]], [[Switzerland]]
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Melfi, Giuseppe}}
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| [[Category:1967 births]]
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| [[Category:20th-century Italian mathematicians]]
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| [[Category:21st-century Italian mathematicians]]
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| [[Category:Living people]]
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| [[Category:Number theorists]]
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| [[Category:Sicilian mathematicians]]
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| [[Category:University of Neuchâtel faculty]]
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Let me first begin by introducing myself. My name is Boyd Butts even though it is not the name on my birth certificate. Hiring is her working day job now but she's always needed her personal company. Years ago we moved to North Dakota. What I love performing is doing ceramics but I haven't made a dime with it.
Here is my web-site - std testing at home (you can look here)