Average prime-pair counting formula

Authors:
Jaap Korevaar and Herman te Riele

Journal:
Math. Comp. **79** (2010), 1209-1229

MSC (2000):
Primary 11P32; Secondary 65-05

DOI:
https://doi.org/10.1090/S0025-5718-09-02312-6

Published electronically:
September 25, 2009

MathSciNet review:
2600563

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Abstract: Taking , let denote the number of prime pairs with . The prime-pair conjecture of Hardy and Littlewood (1923) asserts that with an explicit constant . There seems to be no good conjecture for the remainders that corresponds to Riemann's formula for . However, there is a heuristic approximate formula for averages of the remainders which is supported by numerical results.

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Additional Information

**Jaap Korevaar**

Affiliation:
KdV Institute of Mathematics, University of Amsterdam, Science Park 904, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands

Email:
J.Korevaar@uva.nl

**Herman te Riele**

Affiliation:
CWI: Centrum Wiskunde en Informatica, Science Park 123, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

Email:
Herman.te.Riele@cwi.nl

DOI:
https://doi.org/10.1090/S0025-5718-09-02312-6

Keywords:
Hardy--Littlewood conjecture,
prime-pair functions,
representation by repeated complex integral,
zeta's complex zeros

Received by editor(s):
February 25, 2009

Received by editor(s) in revised form:
June 5, 2009

Published electronically:
September 25, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.