A variational Barban–Davenport–Halberstam Theorem |
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| Authors: | Allison Lewko Mark Lewko |
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| Institution: | 1. Department of Computer Science, The University of Texas at Austin, 1616 Guadalupe, Suite 2.408, Austin, TX 78701, USA;2. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712, USA |
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| Abstract: | We prove variational forms of the Barban–Davenport–Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions. |
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