Structure in the Primes, with applications

Project Information

PRIMES

Grant agreement ID: 851318

DOI

10.3030/851318

Project closed

EC signature date 18 September 2019

Start date 1 February 2020

End date 31 July 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 489 402,00

EU contribution

€ 1 489 402,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (35)

Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor

Author(s): Ofir Gorodetsky, Valeriya Kovaleva
Published in: Bulletin of the London Mathematical Society, Issue 56, 2024, Page(s) 2315-2337, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.13057

On an ErdŐs–Kac-Type Conjecture of Elliott

Author(s): Ofir Gorodetsky, Lasse Grimmelt
Published in: The Quarterly Journal of Mathematics, Issue 75, 2024, Page(s) 695-713, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmath/haae026

Metric theory of Weyl sums

Author(s): Changhao Chen; Bryce Kerr; James Maynard; Igor E. Shparlinski
Published in: Mathematische Annalen, Issue 14321807, 2022, ISSN 1432-1807
Publisher: Springer
DOI: 10.1007/s00208-021-02352-x

Longer Gaps Between Values of Binary Quadratic Forms

Author(s): Rainer Dietmann, Christian Elsholtz, Alexander Kalmynin, Sergei Konyagin, James Maynard
Published in: International Mathematics Research Notices, Issue 16870247, 2022, ISSN 1687-0247
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnac130

On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases

Author(s): Dartyge, C; Maynard, J
Published in: Journal of the European Mathematical Society, Issue 13, 2024, ISSN 1435-9863
Publisher: EMS Publishing House
DOI: 10.48550/arxiv.2212.03381

Squarefrees are Gaussian in short intervals

Author(s): Ofir Gorodetsky, Alexander P. Mangerel, Brad Rodgers
Published in: Journal fur die reine und angewane Mathematik, 2022, ISSN 1435-5345
Publisher: De Gruyter
DOI: 10.1515/crelle-2022-0066

Uniform estimates for friable polynomials over finite fields

Author(s): Ofir Gorodetsky
Published in: Discrete Analysis, 2022, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals

Primes and Polynomials With Restricted Digits

Author(s): James Maynard
Published in: International Mathematics Research Notices, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab002

New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences

Author(s): Ofir Gorodetsky
Published in: Experimental Mathematics, Issue 1944950X, 2021, ISSN 1944-950X
Publisher: Taylor & Francis
DOI: 10.1080/10586458.2021.1982080

Siegel Zeros, Twin Primes, Goldbach’s Conjecture, and Primes in Short Intervals

Author(s): Kaisa Matomäki, Jori Merikoski
Published in: International Mathematics Research Notices, Issue 2023, 2023, Page(s) 20337-20384, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnad069

Sums of two squares are strongly biased towards quadratic residues

Author(s): Ofir Gorodetsky
Published in: Algebra and Number Theory, 2022, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers

Exceptional characters and prime numbers in sparse sets

Author(s): Jori Merikoski
Published in: Algebra and Number Theory, 2023, ISSN 1944-7833
Publisher: Mathematical Sciences Publishers

Multiplicative arithmetic functions and the generalized Ewens measure

Author(s): Dor Elboim, Ofir Gorodetsky
Published in: Israel Journal of Mathematics, 2024, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-024-2609-x

Primes in arithmetic progressions to large moduli I: Fixed residue classes

Author(s): Maynard, James
Published in: Memoirs of the American Mathematical Society, 2023, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2006.06572

The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes

Author(s): Jori Merikoski
Published in: Proceedings of the London Mathematical Society, Issue 127, 2023, Page(s) 1057-1133, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12557

Additive problems with almost prime squares

Author(s): Valentin Blomer, Lasse Grimmelt, Junxian Li, Simon Rydin Myerson
Published in: Geometric and Functional Analysis, 2023, ISSN 1016-443X
Publisher: Birkhauser Verlag

On Gaussian primes in sparse sets

Author(s): Jori Merikoski
Published in: Compositio Mathematica, Issue 161, 2025, Page(s) 181-243, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x24007632

A proof of the Erdős primitive set conjecture

Author(s): Jared Duker Lichtman
Published in: Forum of Mathematics, Pi, Issue 11, 2023, ISSN 2050-5086
Publisher: Cambridge University Press
DOI: 10.1017/fmp.2023.16

Goldbach Numbers in Short Intervals

Author(s): Lasse Grimmelt
Published in: Scuola Normale Superiore, 2023, ISSN 0391-173X
Publisher: Stampacchia Guido

On Erd\H{o}s sums of almost primes

Author(s): Gorodetsky, Ofir; Lichtman, Jared Duker; Wong, Mo Dick
Published in: Comptes Rendus Mathematique, Issue 4, 2024, ISSN 1778-3569
Publisher: Elsevier

Primes in arithmetic progressions to large moduli II: Well-factorable estimates

Author(s): Maynard, J
Published in: Memoirs of the American Mathematical Society, 2023, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2006.07088

A lower bound on the least common multiple of polynomial sequences

Author(s): James Maynard, Zeev Rudnick
Published in: Rivista di Matematica della Università di Parma, Issue Vol 12, Number 1, 2021, Page(s) 143--150, ISSN 2284-2578
Publisher: Department of Mathematics and Computer Science of the University of Parma

Simultaneous Small Fractional Parts of Polynomials

Author(s): James Maynard
Published in: Geometric and Functional Analysis, Issue 31/1, 2021, Page(s) 150-179, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-021-00559-3

Uniform estimates for almost primes over finite fields

Author(s): Dor Elboim, Ofir Gorodetsky
Published in: Proceedings of the American Mathematical Society, Issue 10886826, 2021, ISSN 1088-6826
Publisher: American Mathematical Society
DOI: 10.1090/proc/15870

On the Duffin-Schaeffer Conjecture

Author(s): Dimitris Koukoulopoulos, James Maynard
Published in: Annals of Mathematics, 2020, ISSN 0003-486X
Publisher: Princeton University Press

An almost sharp quantitative version of the Duffin–Schaeffer conjecture

Author(s): Dimitris Koukoulopoulos, James Maynard, Daodao Yang
Published in: Duke Mathematical Journal, Issue 174, 2025, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2024-0055

An almost sharp quantitative version of the Duffin-Schaeffer conjecture

Author(s): Dimtris Koukoulopoulos, James Maynard, Daodao Yang
Published in: Duke Math Journal, 2024, ISSN 1547-7398
Publisher: Duke University Press

A new upper bound for sets with no square differences

Author(s): Bloom, Thomas F.; Maynard, James
Published in: Compositio Mathematica, Issue 15705846, 2022, ISSN 1570-5846
Publisher: London Mathematical Society
DOI: 10.48550/arxiv.2011.13266

Smooth integers and de Bruijn's approximation Ʌ

Author(s): Ofir Gorodetsky
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2024, Page(s) 1-29, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2023.115

Primes in arithmetic progressions to large moduli III: Uniform residue classes

Author(s): Maynard, J
Published in: Memoirs of the American Mathematical Society, 2023, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2006.08250

Magic squares, the symmetric group and Möbius randomness

Author(s): Ofir Gorodetsky
Published in: Monatshefte für Mathematik, Issue 204, 2024, Page(s) 27-46, ISSN 0026-9255
Publisher: Springer Verlag
DOI: 10.1007/s00605-024-01957-z

New large value estimates for Dirichlet polynomials

Author(s): Larry Guth, James Maynard
Published in: Annals of Mathematics, 2025, ISSN 0003-486X
Publisher: Princeton University Press

Uniform estimates for friable polynomials over finite fields

Author(s): Ofir Gorodetsky
Published in: Discrete Analysis, Issue 2, 2023, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals

Smooth integers and the Dickman $ρ$ function

Author(s): Gorodetsky, Ofir
Published in: Journal d'Analyse Mathématique, Issue 4, 2023, ISSN 0021-7670
Publisher: Magnes Press
DOI: 10.48550/arxiv.2211.08973

On the asymmetric additive energy of polynomials

Author(s): Oliver McGrath
Published in: Transactions of the American Mathematical Society, 2024, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9144