{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:53:11Z","timestamp":1791323591617,"version":"4.3.1"},"reference-count":0,"publisher":"Annals of Mathematics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. of Math. (2)"],"published-print":{"date-parts":[[2026,3,1]]},"abstract":"<jats:p>We prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length $N$ taking values of size close to $N^{3\/4}$, which is the critical situation for several estimates in analytic number theory connected to prime numbers and the Riemann zeta function. As a consequence, we deduce a zero density estimate $N(\\sigma,T)\\le T^{30(1-\\sigma)\/13+o(1)}$ and asymptotics for primes in short intervals of length $x^{17\/30+o(1)}$.<\/jats:p>","DOI":"10.4007\/annals.2026.203.2.6","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T06:58:15Z","timestamp":1772434695000},"page":"623-675","source":"Crossref","is-referenced-by-count":8,"title":["New large value estimates for Dirichlet polynomials"],"prefix":"10.4007","volume":"203","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1302-8657","authenticated-orcid":false,"given":"Larry","family":"Guth","sequence":"first","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology, \n\tCambridge, MA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5782-7082","authenticated-orcid":false,"given":"James","family":"Maynard","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, UK and St. John's  College, Oxford, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2422","container-title":["Annals of Mathematics"],"original-title":[],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:31:02Z","timestamp":1791322262000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/annals-of-mathematics\/volume-203\/issue-2\/New-large-value-estimates-for-Dirichlet-polynomials\/10.4007\/annals.2026.203.2.6.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,3,1]]}},"URL":"https:\/\/doi.org\/10.4007\/annals.2026.203.2.6","relation":{},"ISSN":["0003-486X","1939-8980"],"issn-type":[{"value":"0003-486X","type":"print"},{"value":"1939-8980","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,1]]}}}