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French mathematician
Jean-Louis Nicolas is a French
number theorist .
He is the namesake (with
Paul Erdős ) of the
Erdős–Nicolas numbers ,
[1]
[2] and was a frequent co-author of Erdős,
[3] who would take over the desk of Nicolas' wife Anne-Marie (also a mathematician) whenever he would visit.
[4] Nicolas is also known for his research on
integer partitions ,
[4] and for his unusual proof that there exist infinitely many n for which
φ
(
n
)
<
e
−
γ
n
log
log
n
{\displaystyle \varphi (n)<e^{-\gamma }{\frac {n}{\log \log n}}}
where
φ
(
n
)
{\displaystyle \varphi (n)}
is
Euler's totient function and γ is
Euler's constant : he proved this bound unconditionally by providing two different proofs, one in the case that the
Riemann hypothesis holds and another in the case that it fails.
[5]
Nicolas earned his Ph.D. in 1968 as a student of
Charles Pisot .
[6] He works at
Claude Bernard University Lyon 1 .
[7]
A conference in honor of Nicolas' 60th birthday was held on January 14–19, 2002 at the
Centre International de Rencontres Mathématiques in
Marseille . The proceedings of the conference were published as a
festschrift in The Ramanujan Journal .
[8]
References
^ De Koninck, Jean-Marie (2009), Those Fascinating Numbers , p. 141,
ISBN
978-0-8218-4807-4
^
Erdős, P. ;
Nicolas, J.L. (1975),
"Répartition des nombres superabondants" (PDF) , Bull. Soc. Math. France , 79 (103): 65–90,
doi :
10.24033/bsmf.1793 ,
Zbl
0306.10025
^
List of collaborators of Erdős by number of joint papers
Archived 2008-08-04 at the
Wayback Machine , from the Erdős number project web site.
^
a
b Sárközy, A. (2005), "Jean-Louis Nicolas and the partitions", The Ramanujan Journal , 9 (1–2): 7–17,
doi :
10.1007/s11139-005-0820-x ,
MR
2166373 ,
S2CID
119401679 .
^
Ribenboim, Paulo (1996), The New Book of Prime Number Records , New York:
Springer , p. 320,
ISBN
0-387-94457-5 .
^
Jean-Louis Nicolas at the
Mathematics Genealogy Project
^
Jean-Louis Nicolas ,
Claude Bernard University Lyon 1 , retrieved 2015-01-13.
^ "Preface", The Ramanujan Journal , 9 (1–2): 5, 2005,
doi :
10.1007/s11139-005-0819-3 .
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