Vol. 8, No. 9, 2014

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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

Vol. 8 (2014), No. 9, 2067–2199
Abstract

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 1 2 + 7 300.

Keywords
prime gaps, Bombieri–Vinogradov theorem, Elliott–Halberstam conjecture
Mathematical Subject Classification 2010
Primary: 11P32
Milestones
Received: 4 February 2014
Revised: 12 October 2014
Accepted: 12 November 2014
Published: 28 December 2014
Authors
Wouter Castryck
Departement Wiskunde
Katholieke Universiteit Leuven
Celestijnenlaan 200B
3001 Leuven
Belgium
Étienne Fouvry
Laboratoire de Mathématique
Campus d’Orsay, Université de Paris-Sud
Bâtiment 425 UMR 8628
91405 Orsay Cedex
France
Gergely Harcos
Alfréd Rényi Institute of Mathematics
13–15 Reáltanoda utca
H-1053
Budapest
Hungary
Emmanuel Kowalski
Department of Mathematics
ETH Zurich
Rämistrasse 101
CH-8092 Zurich
Switzerland
Philippe Michel
Ecole Polytechnique Fédérale de Lausanne
SB-IMB-TAN, Station 8
CH-1015 Lausanne
Switzerland
Paul Nelson
Department of Mathematics
ETH Zurich
Rämistrasse 101
CH-8092 Zurich
Switzerland
Eytan Paldi
Technion Institute
3200003 Haifa
Israel
János Pintz
Alfréd Rényi Institute of Mathematics
13–15 Reáltanoda utca
H-1053
Budapest
Hungary
Andrew V. Sutherland
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139
United States
Terence Tao
Department of Mathematics
University of California Los Angeles
405 Hilgard Avenue
Los Angeles, CA 90095-1555
United States
Xiao-Feng Xie
The Robotics Institute
Carnegie Mellon University
Pittsburgh, PA 15213
United States