(Mock) Modular Forms are Everywhere

Project Information

ModEv

Grant agreement ID: 101001179

DOI

10.3030/101001179

EC signature date 5 March 2021

Start date 1 September 2021

End date 31 August 2028

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 986 017,00

EU contribution

€ 1 986 017,00

Coordinated by

UNIVERSITAT ZU KOLN
Germany

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 (22)

Odd unimodal sequences

Author(s): Kathrin Bringmann, Jeremy Lovejoy
Published in: Advances in Mathematics, Issue 480, 2025, Page(s) 110458, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110458

Formulas for moments of class numbers in arithmetic progressions

Author(s): Kathrin Bringmann, Ben Kane, Sudhir Pujahari
Published in: Acta Arithmetica, 2022, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.48550/arxiv.2109.07325

Overpartitions with parts separated by parity

Author(s): Kathrin Bringmann, Catherine Cossaboom, William Craig
Published in: Canadian Mathematical Bulletin, 2026, Page(s) 1-11, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439525101616

Periodic sign changes for weakly holomorphic η-quotients

Author(s): Kathrin Bringmann, Guo-Niu Han, Bernhard Heim, Ben Kane
Published in: International Journal of Number Theory, Issue 21, 2025, Page(s) 2111-2139, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042125501027

Improved asymptotics for moments of reciprocal sums for partitions into distinct parts

Author(s): Kathrin Bringmann, Byungchan Kim, Eunmi Kim
Published in: Journal of Combinatorial Theory, Series A, Issue 219, 2026, Page(s) 106119, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2025.106119

Inequalities and asymptotics for hook numbers in restricted partitions

Author(s): William Craig, Madeline Locus Dawsey, Guo–Niu Han
Published in: Journal of Combinatorial Theory, Series A, Issue 221, 2026, Page(s) 106176, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2026.106176

An asymptotic formula for the number of n-dimensional representations of SU(3)

Author(s): Kathrin Bringmann, Johann Franke
Published in: Revista Matematica Iberoamericano, 2022, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.48550/arxiv.2107.03261

Statistics for Unimodal Sequences

Author(s): Bridges, Walter; Bringmann, Kathrin
Published in: Advances in Mathematics, Issue 401, 2022, ISSN 0001-8708
Publisher: Academic Press

Certain infinite products in terms of MacMahon type series

Author(s): Seokho Jin, Badri Vishal Pandey, Ajit Singh
Published in: International Journal of Number Theory, Issue 22, 2026, Page(s) 547-567, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042126500314

Distribution of hooks in self-conjugate partitions

Author(s): William Craig, Ken Ono, Ajit Singh
Published in: Discrete Mathematics, Issue 348, 2025, Page(s) 114563, ISSN 0012-365X
Publisher: Elsevier BV
DOI: 10.1016/j.disc.2025.114563

Asymptotics of parity biases for partitions into distinct parts via Nahm sums

Author(s): Kathrin Bringmann, Siu Hang Man, Larry Rolen, Matthias Storzer
Published in: Proceedings of the London Mathematical Society, Issue 129, 2024, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.70010

Conjectures of Sun about sums of polygonal numbers

Author(s): Kathrin Bringmann; Ben Kane
Published in: La Matematica, Issue 2, 2022, ISSN 2730-9657
Publisher: Springer
DOI: 10.48550/arXiv.2109.14793

Mock modular forms from the k-rank moments

Author(s): Kilian Rausch
Published in: Research in Number Theory, Issue 12, 2026, ISSN 2522-0160
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40993-026-00729-y

Traces of partition Eisenstein series and almost holomorphic modular forms

Author(s): Kathrin Bringmann, Badri Vishal Pandey
Published in: Research in Number Theory, Issue 11, 2025, ISSN 2522-0160
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40993-025-00615-z

Modularity of counting functions of convex planar polygons with rationality conditions

Author(s): Kathrin Bringmann, Jonas Kaszian, Jie Zhou
Published in: Mathematische Annalen, Issue 392, 2025, Page(s) 965-1014, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-024-03087-1

Quasimodularity and limiting behavior for variations of MacMahon series

Author(s): Caner Nazaroglu, Badri Vishal Pandey, Ajit Singh
Published in: Advances in Mathematics, Issue 482, 2025, Page(s) 110565, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110565

On the Asymptotic Behavior for Partitions Separated by Parity

Author(s): Kathrin Bringmann, William Craig, Caner Nazaroglu
Published in: The Electronic Journal of Combinatorics, Issue 32, 2025, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/12886

Distributions on partitions arising from Hilbert schemes and hook lengths

Author(s): Kathrin Bringmann, William Craig, Joshua Males, Ken Ono
Published in: Forum of Mathematics, Sigma, Issue 10, 2022, Page(s) e49, ISSN 2050-5094
Publisher: Robert Guralnick
DOI: 10.48550/arXiv.2109.10394

Iterated integrals and cohomology

Author(s): Kathrin Bringmann, Nikolaos Diamantis
Published in: Journal of Number Theory, Issue 281, 2026, Page(s) 397-425, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2025.09.024

Infinite families of crank functions, Stanton-type conjectures, and unimodality

Author(s): Kathrin Bringmann; Kevin Gomez; Larry Rolen; Zack Tripp
Published in: Research in the Mathematical Sciences, Issue 3, 2022, ISSN 2197-9847
Publisher: Springer
DOI: 10.1007/s40687-022-00333-3

On a sign-change conjecture of Schlosser and Zhou

Author(s): Kathrin Bringmann, Bernhard Heim, Ben Kane
Published in: Journal of Mathematical Analysis and Applications, Issue 548, 2025, Page(s) 129339, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2025.129339

Modularity of moments of reciprocal sums for partitions into distinct parts

Author(s): Kathrin Bringmann, Byungchan Kim, Eunmi Kim
Published in: Research in the Mathematical Sciences, Issue 12, 2025, ISSN 2522-0144
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40687-025-00536-4

Non-peer reviewed articles (19)

Integer partitions detect the primes

Author(s): William Craig, Jan-Willem van Ittersum, Ken Ono
Published in: Proceedings of the National Academy of Sciences, Issue 121, 2024, ISSN 0027-8424
Publisher: National Academy of Sciences
DOI: 10.1073/pnas.2409417121

Fractional partitions and conjectures of Chern–Fu–Tang andHeim–Neuhauser

Author(s): K. Bringmann, B. Kane, L. Rolen, and Z. Tripp
Published in: Transactions of the American Mathematical Society, Series B, Issue 8, 2021, Page(s) 615-634, ISSN 2330-0000
Publisher: AMS
DOI: 10.48550/arxiv.2011.08874

On a Tauberian theorem of Ingham and Euler-Maclaurinsummation

Author(s): K. Bringmann, C. Jennings-Shaffer, and K. Mahlburg
Published in: The Ramanujan Journal, 2021, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-020-00377-5

On the number of irreducible representations of su(3)

Author(s): W. Bridges, K. Bringmann, and J. Franke
Published in: Acta Arithmetica, 2023, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.48550/arxiv.2308.02319

Integral representations of rank two false theta functionsand their modularity properties

Author(s): K. Bringmann, J. Kaszian, A. Milas, and C. Nazaroglu
Published in: the Mathematical Sciences, Issue 8:54, 2021, ISSN 2522-0144
Publisher: Springer
DOI: 10.1007/s40687-021-00284-1

Asymptotic expansions for partitions generated by infiniteproducts,

Author(s): W. Bridges, B. Brindle, K. Bringmann, and J. Franke
Published in: Mathematische Annalen, 2024, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-024-02807-x

Massive deformations of Maass forms and Jacobi forms

Author(s): K. Bringmann, M. Berg, and T. Gannon
Published in: Communication in Number Theory and Physics, Issue 15:3, 2021, Page(s) 575-603, ISSN 1931-4523
Publisher: International Press of Boston, Inc.
DOI: 10.4310/cntp.2021.v15.n3.a4

Log-concavity for unimodal sequences

Author(s): W. Bridges and K. Bringmann
Published in: Number Theory, Issue 10, 2024, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.48550/arxiv.2307.05120

Distributions on partitions arising from Hilbert schemes andHook lengths

Author(s): K. Bringmann, W. Craig, J. Males, and K. Ono
Published in: Forum of Mathematics Sigma, Issue 10 E49, 2022, Page(s) 1-130, ISSN 2050-5094
Publisher: Cambridge Core
DOI: 10.48550/arxiv.2109.10394

Eichler integrals of Eisenstein series as q-brackets of weighted t-hookfunctions on partitions

Author(s): K. Bringmann, K. Ono, and I. Wagner
Published in: Ramanujan Journal, 2021, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.48550/arxiv.2009.07236

Class numbers and representations by ternary quadratic forms with congruenceconditions

Author(s): K. Bringmann and B. Kane
Published in: Mathematics of Computation, Issue 91, 2022, ISSN 1088-6842
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2002.01835

On t-core and self-conjugate (2t − 1)-core partitions in arithmetic pro-gressions

Author(s): K. Bringmann, B. Kane, and J. Males
Published in: Journal of Combinatorial Theory Series A, Issue 183, 2021, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.48550/arxiv.2005.07020

Hook length biases and general linear partition inequalities

Author(s): Cristina Ballantine, Hannah Burson, William Craig, Amanda Folsom, Boya Wen
Published in: Mathematical Sciences, Band 10, 41, 2023, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2303.16512

Biases among classes of rank-crank partitions (mod 11)

Author(s): K. Bringmann and B. Pandey
Published in: journal of Mathematical Analysis and Applications, Issue Volume 536, 2024, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.48550/arxiv.2308.02327

Asymptotics of commuting $$\ell $$-tuples in symmetric groups and log-concavity

Author(s): Kathrin Bringmann, Johann Franke, Bernhard Heim
Published in: Research in Number Theory, Issue 10, 2024, ISSN 2522-0160
Publisher: Springer
DOI: 10.1007/s40993-024-00562-1

An asymptotic formula for the number of n-dimensional representations of SU(3)

Author(s): Kathrin Bringmann, Johann Franke
Published in: Revista Matem´atica Iberoamericana, Issue 39, 2023, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.48550/arxiv.2107.03261

A Rademacher-type exact formula for partitions without sequences

Author(s): Walter Bridges, Kathrin Bringmann
Published in: The Quarterly Journal of Mathematics, Issue 75, 2024, Page(s) 197-217, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.48550/arxiv.2304.01377

Asymptotic equidistribution for partition statistics and topological invariants

Author(s): Giulia Cesana, William Craig, Joshua Males
Published in: Journal of Number Theory, Issue 256, 2023, Page(s) 373-396, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2023.10.007

Taylor coefficients of false Jacobi forms and ranks of unimodal sequences

Author(s): W. Bridges and K. Bringmann
Published in: Advances in Mathematics, Issue 426, 2023, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.48550/arxiv.2208.11942