Daniel Goldston

Daniel Goldston
Daniel Goldston
Biographie
Naissance
Voir et modifier les données sur Wikidata (71 ans)
OaklandVoir et modifier les données sur Wikidata
Surnom
DanVoir et modifier les données sur Wikidata
Nationalité
Formation
Activités
Autres informations
A travaillé pour
Membre de
Directeur de thèse
Russell Sherman Lehman (d)Voir et modifier les données sur Wikidata
Distinctions

modifier - modifier le code - modifier WikidataDocumentation du modèle

Daniel Alan Goldston, né le à Oakland (Californie), est un mathématicien américain spécialiste de théorie analytique des nombres. Il est professeur à l'université d'État de San José.

Biographie

Goldston obtient son Ph. D. de l'université de Californie à Berkeley, sous la direction de R. Sherman Lehman. Son nombre d'Erdős est 2.

Daniel Goldston est surtout connu pour le résultat suivant, qu'il a démontré en 2005 avec János Pintz et Cem Yıldırım[1] :

où pn désigne le ne nombre premier. Autrement dit, pour tout réel c > 0, il existe une infinité de couples de nombres premiers consécutifs pn et pn+1 dont la distance est inférieure au produit par c de la distance moyenne, dans cette zone, entre deux nombres premiers consécutifs, c'est-à-dire tels que pn+1 – pn < c log pn.

Goldston et Yıldırım annoncent ce résultat en 2003 puis se sont rétractés[2]. Pintz rejoint l'équipe et ils achèvent la preuve en 2005.

En fait, en supposant vraie la conjecture d'Elliott-Halberstam, ils montrent aussi qu'il y a une infinité de couples de nombres premiers consécutifs à distance au plus 16 l'un de l'autre, ce qui est un progrès vers la conjecture des nombres premiers jumeaux.

Notes et références

(en) Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé « Daniel Goldston » (voir la liste des auteurs).
  1. ↑ (en) D. A. Goldston, J. Pintz et C. Y. Yildirim, « Primes in Tuples I », Ann. Math., vol. 170,‎ , p. 819-862, preprint de 2005 sur arXiv:math/0508185
  2. ↑ (en) « May 2005: Breakthrough in Prime Number theory », sur American Institute of Mathematics (en)

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