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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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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DOI: https://doi.org/10.1007/978-0-8176-8334-4_12
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