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A Pseudo Twin Primes Theorem

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Multiple Dirichlet Series, L-functions and Automorphic Forms

Part of the book series: Progress in Mathematics ((PM,volume 300))

Abstract

Selberg identified the “parity” barrier that sieves alone cannot distinguish between integers having an even or odd number of factors. We give here a short and self-contained demonstration of parity breaking using bilinear forms, modeled on the twin primes conjecture.

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Acknowledgments

The author wishes to thank Peter Sarnak for suggesting this problem, and generously lending of his time. Thanks also to Dorian Goldfeld and Patrick Gallagher for enlightening conversations, and to Tim Browning, Gautam Chinta, Steven J. Miller, and the referee for corrections to an earlier draft.

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Authors and Affiliations

  1. Mathematics Department, Yale University, 208283, New Haven, CT, 06520-8283, USA

    Alex V. Kontorovich

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  1. Alex V. Kontorovich
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Correspondence to Alex V. Kontorovich .

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Editors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, 94305-2125, California, USA

    Daniel Bump

  2. , Department of Mathematics, Boston College, Commonwealth Ave. 140, Chestnut Hill, 02467-3806, Massachusetts, USA

    Solomon Friedberg

  3. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

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Kontorovich, A.V. (2012). A Pseudo Twin Primes Theorem. In: Bump, D., Friedberg, S., Goldfeld, D. (eds) Multiple Dirichlet Series, L-functions and Automorphic Forms. Progress in Mathematics, vol 300. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8334-4_12

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