Random Models in Arithmetic and Spectral Theory

Project Information

RMAST

Grant agreement ID: 786758

DOI

10.3030/786758

Project closed

EC signature date 10 April 2018

Start date 1 February 2019

End date 31 January 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 840 625,00

EU contribution

€ 1 840 625,00

Coordinated by

TEL AVIV UNIVERSITY
Israel

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 (43)

Pointwise bounds for Eisenstein series on $\Gamma_0(q)\setminus SL_2(\mathbb{R})$

Author(s): Musicantov, Evgeny; Zehavi, Sa'ar
Published in: The Quarterly Journal of Mathematics, Issue 3, 2023, Page(s) 529–591, ISSN 1464-3847
Publisher: Oxford University Press
DOI: 10.1093/qmath/haac032

On the Robin spectrum for the hemisphere

Author(s): Zeév Rudnick, Igor Wigman
Published in: Annales mathématiques du Québec, 2021, ISSN 2195-4763
Publisher: Springer
DOI: 10.1007/s40316-021-00155-9

The quantum Rabi model: towards Braak’s conjecture

Author(s): Zeév Rudnick
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 57, 2024, Page(s) 285206, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ad5ac6

Effective joint equidistribution of primitive rational points on expanding horospheres

Author(s): Daniel El-Baz, Bingrong Huang, Min Lee
Published in: Journal of the European Mathematical Society, Issue 25, 2025, Page(s) 2295-2317, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1238

On Quantum Ergodicity for Higher Dimensional Cat Maps

Author(s): Pär Kurlberg, Alina Ostafe, Zeev Rudnick, Igor E. Shparlinski
Published in: Communications in Mathematical Physics, Issue 406, 2025, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-025-05350-1

Vanishing of Poincare series for congruence subgroups

Author(s): Noam Kimmel
Published in: Hardy-Ramanujan Journal, Issue Volume 47 - 2024, 2025, Page(s) 35-43, ISSN 2804-7370
Publisher: Centre pour la Communication Scientifique Directe (CCSD)
DOI: 10.46298/hrj.2025.15573

On the correlations of $n^\alpha$ mod 1

Author(s): Technau, Niclas; Yesha, Nadav
Published in: J. Eur. Math. Soc., Issue 3, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1281

Uniform estimates for almost primes over finite fields

Author(s): Dor Elboim, Ofir Gorodetsky
Published in: Proceedings of the American Mathematical Society, Issue 150, 2022, Page(s) 2807-2822, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15870

Uniform estimates for smooth polynomials over finite fields

Author(s): Gorodetsky, O
Published in: Discrete Analysis, Issue 4, 2023, ISSN 2397-3129
Publisher: Alliance of Diamond Open Access Journals
DOI: 10.19086/da.87773

Mass Equidistribution for Poincaré Series of Large Index

Author(s): Noam Kimmel
Published in: The Quarterly Journal of Mathematics, Issue 76, 2025, Page(s) 265-285, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmath/haae071

The Robin problem on rectangles

Author(s): Rudnick, Zeév; Wigman, Igor
Published in: J. Math. Phys., Issue 7, 2021, Page(s) 113503, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0061763

Almost Sure GOE Fluctuations of Energy Levels for Hyperbolic Surfaces of High Genus

Author(s): Zeév Rudnick, Igor Wigman
Published in: Annales Henri Poincaré, Issue 26, 2025, Page(s) 2279-2291, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-025-01552-4

Modelling the expected probability of correct assignment under uncertainty

Author(s): Tom Dvir, Renana Peres, Zeév Rudnick
Published in: Scientific Reports, Issue 10/1, 2020, ISSN 2045-2322
Publisher: Nature Publishing Group
DOI: 10.1038/s41598-020-71558-x

Asymptotic Zeros of Poincaré Series

Author(s): Noam Kimmel
Published in: International Mathematics Research Notices, Issue 2024, 2024, Page(s) 13808-13826, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnae224

Consecutive runs of sums of two squares

Author(s): Noam Kimmel, Vivian Kuperberg
Published in: Journal of Number Theory, Issue 264, 2024, Page(s) 135-147, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2024.05.003

The metric theory of the pair correlation function of real-valued lacunary sequences

Author(s): Zeév Rudnick, Niclas Technau
Published in: Illinois Journal of Mathematics, Issue 64/4, 2020, ISSN 0019-2082
Publisher: University of Illinois at Urbana-Champaign, Department of Mathematics
DOI: 10.1215/00192082-8720506

Sectorial Equidistribution of the Roots of <i>x</i>2 + 1 Modulo Primes

Author(s): Evgeny Musicantov, Sa’ar Zehavi
Published in: The Quarterly Journal of Mathematics, Issue 75, 2024, Page(s) 563-611, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmath/haae011

Traces of powers of matrices over finite fields

Author(s): Ofir Gorodetsky, Brad Rodgers
Published in: Transactions of the American Mathematical Society, Issue 374/7, 2021, Page(s) 4579-4638, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8337

The metric theory of the pair correlation function for small non‐integer powers

Author(s): Zeév Rudnick; Niclas Technau
Published in: Journal of the London Mathematical Society, Issue 1, 2022, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12647

On a family of sparse exponential sums

Author(s): Moubariz Z. Garaev, Zeev Rudnick, Igor E. Shparlinski
Published in: Mathematische Nachrichten, Issue 297, 2024, Page(s) 4214-4231, ISSN 0025-584X
Publisher: Wiley - V C H Verlag GmbbH & Co.
DOI: 10.1002/mana.202300426

Artin’s primitive root conjecture in number fields and for matrices

Author(s): Noam Kimmel
Published in: Acta Arithmetica, Issue 216, 2024, Page(s) 329-348, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa230810-29-6

A lower bound on the LCM of polynomial sequences

Author(s): Maynard, James; Rudnick, Zeev
Published in: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA, Issue 3, 2021, Page(s) 143-150, ISSN 0035-6298
Publisher: Universita degli Studi di Parma

Covariance of Error Terms Related to the Dirichlet Eigenvalue Problem

Author(s): Noam Kimmel
Published in: Mathemtika, Issue 6, 2022, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.12126

POSITIVE DENSITY FOR CONSECUTIVE RUNS OF SUMS OF TWO SQUARES

Author(s): Noam Kimmel, Vivian Kuperberg
Published in: Journal of the Institute of Mathematics of Jussieu, Issue 24, 2025, Page(s) 1995-2046, ISSN 1474-7480
Publisher: Cambridge University Press
DOI: 10.1017/s1474748025000131

A lower bound on the LCM of polynomial sequences

Author(s): Maynard, James; Rudnick, Zeev
Published in: Rivista di Matematica della Universita di Parma, Issue 5, 2021, ISSN 0035-6298
Publisher: Universita degli Studi di Parma
DOI: 10.48550/arxiv.1910.13218

Angles of Gaussian primes

Author(s): Zeév Rudnick, Ezra Waxman
Published in: Israel Journal of Mathematics, Issue 232/1, 2019, Page(s) 159-199, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-019-1867-5

Gaussian primes in almost all narrow sectors

Author(s): Bingrong Huang, Jianya Liu, Zeév Rudnick
Published in: Acta Arithmetica, Issue 193/2, 2020, Page(s) 183-192, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa190331-23-7

On the Zeros of the Miller Basis of Cusp Forms

Author(s): Roei Raveh
Published in: Research in Number Theory, Issue 11, 2025, ISSN 2522-0160
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40993-025-00679-x

Differences between Robin and Neumann eigenvalues

Author(s): Zeev Rudnick, Igor Wigman, Nadav Yesha
Published in: Commun. Math. Phys., Issue 1, 2021, Page(s) 1603–1635, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04248-y

Gap statistics and higher correlations for geometric progressions modulo one

Author(s): Christoph Aistleitner, Simon Baker, Niclas Technau, Nadav Yesha
Published in: Mathematische Annalen, Issue 385, 2023, Page(s) 845-861, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-022-02362-3

On the Central Limit Theorem for linear eigenvalue statistics on random surfaces of large genus

Author(s): Zeév Rudnick, Igor Wigman
Published in: Journal d'Analyse Mathématique, Issue 151, 2023, Page(s) 293-302, ISSN 0021-7670
Publisher: Magnes Press
DOI: 10.1007/s11854-023-0327-7

The least common multiple of a bivariate quadratic sequence

Author(s): Noam Kimmel
Published in: Acta Arithmetica, Issue 211, 2023, Page(s) 25-60, ISSN 0065-1036
Publisher: Polska Akademia Nauk
DOI: 10.4064/aa220719-9-7

On the variance of squarefree integers in short intervals and arithmetic progressions

Author(s): Ofir Gorodetsky; Kaisa Matomäki; Maksym Radziwiłł; Brad Rodgers
Published in: Geometric and Functional Analysis, Issue 11, 2021, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-021-00557-5

Pair arithmetical equivalence for quadratic fields

Author(s): Wen-Ching Winnie Li, Zeev Rudnick
Published in: Mathematische Zeitschrift, 2021, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02706-w

On Cilleruelo’s conjecture for the least common multiple of polynomial sequences

Author(s): Zeév Rudnick, Sa'ar Zehavi
Published in: Revista Matemática Iberoamericana, Issue 37/4, 2021, Page(s) 1441-1458, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1234

On the order of magnitude of Sudler products

Author(s): Aistleitner, Christoph; Technau, Niclas; Zafeiropoulos, Agamemnon
Published in: American Journal of Mathematics, Issue 4, 2023, ISSN 0002-9327
Publisher: The Johns Hopkins University Press
DOI: 10.1353/ajm.2023.a897495

Points on nodal lines with given direction

Author(s): Zeév Rudnick, Igor Wigman
Published in: Journal of Spectral Theory, Issue 10/3, 2020, Page(s) 927-953, ISSN 1664-039X
Publisher: EMS Press
DOI: 10.4171/jst/317

Quantum Variance for Eisenstein Series

Author(s): Bingrong Huang
Published in: International Mathematics Research Notices, Issue 2021/2, 2019, Page(s) 1224-1248, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnz304

GOE statistics on the moduli space of surfaces of large genus

Author(s): Zeév Rudnick
Published in: Geometric and Functional Analysis, Issue 33, 2024, Page(s) 1581-1607, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-023-00655-6

Multiplicative arithmetic functions and the generalized Ewens measure

Author(s): Dor Elboim, Ofir Gorodetsky
Published in: Israel Journal of Mathematics, Issue 262, 2024, Page(s) 143-189, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-024-2609-x

Zeros of modular forms and Faber polynomials

Author(s): Zeév Rudnick
Published in: Mathematika, Issue 70, 2024, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.12244

On the Robin spectrum for the equilateral triangle

Author(s): Zeev Rudnick; Igor Wigman
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 3, 2022, Page(s) 254004, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac6f9b

Minimal gaps and additive energy in real-valued sequences

Author(s): Shvo Regavim
Published in: The Quarterly Journal of Mathematics, Issue 74, 2023, Page(s) 825-866, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmath/haac043