(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 (51)

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

Distributions of parity differences and biases in partitions into distinct parts

Author(s): Siu Hang Man
Published in: European Journal of Combinatorics, Issue 127, 2025, Page(s) 104157, ISSN 0195-6698
Publisher: Academic Press
DOI: 10.1016/j.ejc.2025.104157

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

On the distribution of the norm of partitions

Author(s): Walter Bridges, William Craig
Published in: The Ramanujan Journal, Issue 66, 2025, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-024-00969-5

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

Author(s): Kathrin Bringmann, Ben Kane, Larry Rolen, Zack Tripp
Published in: Transactions of the American Mathematical Society, Series B, Issue 8, 2026, Page(s) 615-634, ISSN 2330-0000
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/btran/77

On a Tauberian theorem of Ingham and Euler-Maclaurin summation

Author(s): Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg
Published in: The Ramanujan Journal, Issue 61, 2021, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-020-00377-5

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

Graph schemes, graph series, and modularity

Author(s): Kathrin Bringmann, Chris Jennings-Shaffer, Antun Milas
Published in: Journal of Combinatorial Theory, Series A, Issue 197, 2025, Page(s) 105749, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2023.105749

On the number of irreducible representations of $\mathfrak{su}(3)$

Author(s): Walter Bridges, Kathrin Bringmann, Johann Franke
Published in: Acta Arithmetica, Issue 215, 2024, Page(s) 65-71, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa230813-9-4

Integral representations of rank two false theta functions and their modularity properties

Author(s): Kathrin Bringmann, Jonas Kaszian, Antun Milas, Caner Nazaroglu
Published in: Research in the Mathematical Sciences, Issue 8, 2021, ISSN 2522-0144
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40687-021-00284-1

Odd moments for the trace of Frobenius and the Sato–Tate conjecture in arithmetic progressions

Author(s): Kathrin Bringmann, Ben Kane, Sudhir Pujahari
Published in: Finite Fields and Their Applications, Issue 98, 2024, Page(s) 102465, ISSN 1071-5797
Publisher: Academic Press
DOI: 10.1016/j.ffa.2024.102465

Asymptotic expansions for partitions generated by infinite products

Author(s): Walter Bridges, Benjamin Brindle, Kathrin Bringmann, Johann Franke
Published in: Mathematische Annalen, Issue 390, 2024, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-024-02807-x

Massive deformations of Maass forms and Jacobi forms

Author(s): Marcus Berg, Kathrin Bringmann, Terry 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

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

Bounds for Kloosterman sums on $$\textrm{GL}(n)$$

Author(s): Valentin Blomer, Siu Hang Man
Published in: Mathematische Annalen, Issue 390, 2024, Page(s) 1171-1200, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-023-02777-6

Log concavity for unimodal sequences

Author(s): Walter Bridges, Kathrin Bringmann
Published in: Research in Number Theory, Issue 10, 2024, ISSN 2522-0160
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40993-023-00490-6

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

Author(s): Kathrin Bringmann, Ken Ono, Ian Wagner
Published in: The Ramanujan Journal, Issue 61, 2023, Page(s) 279-293, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-021-00453-4

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

Proving dualities for $q$MZVs with connected sums

Author(s): Benjamin Brindle
Published in: Proceedings of the Japan Academy, Series A, Mathematical Sciences, Issue 98, 2022, ISSN 0386-2194
Publisher: Nippon Gakushiin/Japan Academy
DOI: 10.3792/pjaa.98.006

Class numbers and representations by ternary quadratic forms with congruence conditions

Author(s): Kathrin Bringmann, Ben Kane
Published in: Mathematics of Computation, Issue 91, 2021, Page(s) 295-329, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3648

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

Vanishing properties of Fourier coefficients of holomorphic η-quotients

Author(s): Kathrin Bringmann, Guoniu Han, Bernhard Heim, Ben Kane
Published in: Acta Arithmetica, Issue 220, 2025, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa250119-3-7

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

Author(s): Kathrin Bringmann, Johann Franke
Published in: Revista Matemática Iberoamericana, Issue 39, 2025, Page(s) 1599-1640, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1415

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

Author(s): Kathrin Bringmann, Ben Kane, Joshua Males
Published in: Journal of Combinatorial Theory, Series A, Issue 183, 2025, Page(s) 105479, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2021.105479

Hook length biases and general linear partition inequalities

Author(s): Cristina Ballantine, Hannah E. Burson, William Craig, Amanda Folsom, Boya Wen
Published in: Research in the Mathematical Sciences, Issue 10, 2023, ISSN 2522-0144
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40687-023-00402-1

Statistics for unimodal sequences

Author(s): Walter Bridges, Kathrin Bringmann
Published in: Advances in Mathematics, Issue 401, 2025, Page(s) 108288, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108288

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

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

Author(s): Kathrin Bringmann, Badri Vishal Pandey
Published in: Journal of Mathematical Analysis and Applications, Issue 536, 2025, Page(s) 128221, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2024.128221

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 for d-Fold Partition Diamonds and Related Infinite Products

Author(s): Kathrin Bringmann, William Craig, Joshua Males
Published in: Michigan Mathematical Journal, Issue -1, 2026, ISSN 0026-2285
Publisher: University Of Michigan, Department of Mathematics
DOI: 10.1307/mmj/20236485

Exact formula for cubic partitions

Author(s): Lukas Mauth
Published in: The Ramanujan Journal, Issue 64, 2024, ISSN 1572-9303
Publisher: Springer Nature
DOI: 10.21203/rs.3.rs-3227533/v1

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

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

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: 10.1093/qmath/haad043

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

Conjectures of Sun About Sums of Polygonal Numbers

Author(s): Kathrin Bringmann, Ben Kane
Published in: La Matematica, Issue 1, 2023, Page(s) 809-828, ISSN 2730-9657
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s44007-022-00030-1

Flipping operators and locally harmonic Maass forms

Author(s): Kathrin Bringmann, Andreas Mono, Larry Rolen
Published in: The Ramanujan Journal, Issue 68, 2025, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-025-01183-7

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

Taylor coefficients of false Jacobi forms and ranks of unimodal sequences

Author(s): Walter Bridges, Kathrin Bringmann
Published in: Advances in Mathematics, Issue 426, 2025, Page(s) 109074, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2023.109074

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

Jacobi forms with CM and applications

Author(s): Ian Wagner
Published in: Journal of Number Theory, Issue 246, 2025, Page(s) 15-48, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2022.11.014

The Riemann hypothesis for period polynomials of cusp forms

Author(s): William Craig, Wissam Raji
Published in: Acta Arithmetica, Issue 218, 2025, Page(s) 175-195, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa240320-16-9

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 (2)

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

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