Upper bounds for prime k-tuples of size log N and oscillations

Christian Elsholtz

doi:10.1007/s00013-003-4780-3

Upper bounds for prime k-tuples of size log N and oscillations

Christian Elsholtz^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

We prove the estimate E_k ≪ N/exp((1/4 + o(1)) log N log log log N/log log N), for the number E_k (N) of k-tuples (n + a ₁, . . ., n + a_k) of primes not exceeding N, for k of size c₁ log N and N sufficiently large. A bound of this strength was previously known in the special case n - 2ⁱ (1 ≦ i <log n/log 2) only, (Vaughan, 1973). For general a_i this is an improvement upon the work of Hofmann and Wolke (1996). The number of prime tuples of this size has considerable oscillations, when varying the prime pattern.

Originalsprache	englisch
Seiten (von - bis)	33-39
Seitenumfang	7
Fachzeitschrift	Archiv der Mathematik
Jahrgang	82
Ausgabenummer	1
DOIs	https://doi.org/10.1007/s00013-003-4780-3
Publikationsstatus	Veröffentlicht - Jan. 2004

ASJC Scopus subject areas

Allgemeine Mathematik

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10.1007/s00013-003-4780-3

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Upper bounds for prime k-tuples of size log N and oscillations

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