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BIG BIASES AMONGST PRODUCTS OF TWO PRIMES

Part of: Exponential sums and character sums Multiplicative number theory

Published online by Cambridge University Press:  18 February 2016

David Dummit ,
Andrew Granville  and
Hershy Kisilevsky
David Dummit
Affiliation:
Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, U.S.A. email [email protected]
Andrew Granville
Affiliation:
Département de mathématiques et de statistiques, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal, QC H3C 3J7, Canada Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, [email protected]
Hershy Kisilevsky
Affiliation:
Department of Mathematics and Statistics, Sir George Williams Campus, Concordia University, Montreal, QC H3G 1M8, Canada email [email protected]
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Abstract

We show that substantially more than a quarter of the odd integers of the form $pq$ up to $x$, with $p,q$ both prime, satisfy $p\equiv q\equiv 3~(\text{mod}\,4)$.

MSC classification

Primary: 11L20: Sums over primes 11N25: Distribution of integers with specified multiplicative constraints 11N13: Primes in progressions
Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 502 - 507
Copyright
Copyright © University College London 2016 

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References

Ford, K. and Sneed, J., Chebyshev’s bias for products of two primes. Exp. Math. 19 2010, 385–398.Google Scholar
Granville, A. and Soundararajan, K., The distribution of values of L (1, 𝜒 d ). Geom. Funct. Anal. 13 2003, 992–1028.Google Scholar