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New
equidistribution estimates of Zhang type
Wouter Castryck, Étienne Fouvry, Gergely Harcos, Emmanuel Kowalski, Philippe Michel, Paul Nelson, Eytan Paldi, János Pintz, Andrew V. Sutherland, Terence Tao and Xiao-Feng Xie |
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Vol. 8 (2014), No. 9, 2067–2199
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Abstract |
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We prove distribution estimates for primes in arithmetic progressions to large smooth squarefree moduli, with respect to congruence classes obeying Chinese remainder theorem conditions, obtaining an exponent of distribution . |
Keywords
prime gaps, Bombieri–Vinogradov theorem, Elliott–Halberstam
conjecture
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Mathematical Subject Classification 2010
Primary: 11P32
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Milestones
Received: 4 February 2014
Revised: 12 October 2014
Accepted: 12 November 2014
Published: 28 December 2014
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Authors |
| Wouter Castryck | |
| Departement Wiskunde Katholieke Universiteit Leuven Celestijnenlaan 200B 3001 Leuven Belgium |
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| Étienne Fouvry | |
| Laboratoire de Mathématique Campus d’Orsay, Université de Paris-Sud Bâtiment 425 UMR 8628 91405 Orsay Cedex France |
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| Gergely Harcos | |
| Alfréd Rényi Institute of
Mathematics 13–15 Reáltanoda utca H-1053 Budapest Hungary |
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| Emmanuel Kowalski | |
| Department of Mathematics ETH Zurich Rämistrasse 101 CH-8092 Zurich Switzerland |
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| Philippe Michel | |
| Ecole Polytechnique Fédérale de
Lausanne SB-IMB-TAN, Station 8 CH-1015 Lausanne Switzerland |
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| Paul Nelson | |
| Department of Mathematics ETH Zurich Rämistrasse 101 CH-8092 Zurich Switzerland |
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| Eytan Paldi | |
| Technion Institute 3200003 Haifa Israel |
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| János Pintz | |
| Alfréd Rényi Institute of
Mathematics 13–15 Reáltanoda utca H-1053 Budapest Hungary |
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| Andrew V. Sutherland | |
| Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 United States |
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| Terence Tao | |
| Department of Mathematics University of California Los Angeles 405 Hilgard Avenue Los Angeles, CA 90095-1555 United States |
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| Xiao-Feng Xie | |
| The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 United States |
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