Functiones et Approximatio Commentarii Mathematici

The tail of the singular series for the prime pair and Goldbach problems

Daniel A. Goldston, Timothy Ngotiaoco, and Julian Ziegler Hunts

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We obtain an asymptotic formula for a weighted sum of the square of the tail in the singular series for the Goldbach and prime-pair problems.

Article information

Funct. Approx. Comment. Math. Volume 56, Number 1 (2017), 117-141.

First available in Project Euclid: 27 January 2017

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Digital Object Identifier

Primary: 11N05: Distribution of primes
Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes 11N36: Applications of sieve methods

Hardy-Littlewood conjecture prime numbers singular series


Goldston, Daniel A.; Ziegler Hunts, Julian; Ngotiaoco, Timothy. The tail of the singular series for the prime pair and Goldbach problems. Funct. Approx. Comment. Math. 56 (2017), no. 1, 117--141. doi:10.7169/facm/1602.

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