### 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 c_{1} log N and N sufficiently large. A bound of this strength was previously known in the special case n - 2^{i} (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.

Original language | English |
---|---|

Pages (from-to) | 33-39 |

Number of pages | 7 |

Journal | Archiv der Mathematik |

Volume | 82 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2004 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Upper bounds for prime k-tuples of size log N and oscillations.** / Elsholtz, Christian.

Research output: Contribution to journal › Article › Research › peer-review

*Archiv der Mathematik*, vol. 82, no. 1, pp. 33-39. https://doi.org/10.1007/s00013-003-4780-3

}

TY - JOUR

T1 - Upper bounds for prime k-tuples of size log N and oscillations

AU - Elsholtz, Christian

PY - 2004/1

Y1 - 2004/1

N2 - We prove the estimate Ek ≪ N/exp((1/4 + o(1)) log N log log log N/log log N), for the number Ek (N) of k-tuples (n + a 1, . . ., n + ak) 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 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.

AB - We prove the estimate Ek ≪ N/exp((1/4 + o(1)) log N log log log N/log log N), for the number Ek (N) of k-tuples (n + a 1, . . ., n + ak) 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 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.

UR - http://www.scopus.com/inward/record.url?scp=1142300714&partnerID=8YFLogxK

U2 - 10.1007/s00013-003-4780-3

DO - 10.1007/s00013-003-4780-3

M3 - Article

VL - 82

SP - 33

EP - 39

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 1

ER -