Prof Abhishek Saha
Professor of Mathematics
REF and Reputation Lead
School of Mathematical Sciences
Queen Mary University of London
Queen Mary University of London
Research
automorphic forms, number theory, Siegel modular forms, L-functions
Interests
My research interests lie in number theory and automorphic forms. My current research has two main directions: algebraic (arithmetic of L-functions, representation theory of p-adic and real groups, functoriality, explicit Gan–Gross–Prasad period formulas) and analytic (sup-norms of automorphic forms, subconvex bounds on central L-values, estimates of Fourier coefficients, Quantum Unique Ergodicity).I am on the editorial board of JLMS and BLMS.
Publications
Publications of specific relevance to the Centre for Combinatorics, Algebra and Number Theory2025
Bounds on Fourier coefficients and global sup‐norms for Siegel cusp forms of degree 2Comtat F Marzec‐Ballesteros J Saha A
Journal of The London Mathematical Society, Wiley vol. 111 (3)
01-03-2025
2024
Mass Equidistribution for Saito-Kurokawa LiftsJääsaari J Lester S Saha A
Geometric and Functional Analysis, Springer Nature vol. 34 (5), 1460-1532.
23-07-2024
Mass equidistribution for Saito-Kurokawa liftsJääsaari J Lester S Saha A
In Arxiv
03-07-2024
Equality, Diversity and Inclusion in the Mathematics Community: A Perspective on Data and PolicySaha A
European Review, Cambridge University Press (Cup) vol. 32 (3), 308-320.
01-06-2024
2023
The Manin constant and the modular degreeCesnavicius K Neururer M Saha A
Journal of The European Mathematical Society, Ems Press
15-09-2023
Simple supercuspidal representations of $\mathrm{GSp}_4$ and test vectorsPitale A Saha A Schmidt R
In Arxiv
10-02-2023
2022
On Fourier coefficients and Hecke eigenvalues of Siegel cusp forms of
degree 2Paul B Saha A
International Mathematics Research Papers, Oxford University Press
15-11-2022
The special values of the standard L-functions for GSp2n × GL1Horinaga S Pitale A Saha A Schmidt R
Transactions of The American Mathematical Society, American Mathematical Society
29-07-2022
2020
Sup-norms of eigenfunctions in the level aspect for compact arithmetic
surfaces, II: newforms and subconvexityHu Y Saha A
Compositio Mathematica, Foundation Compositio Mathematica
01-11-2020
On the standard $L$-function for $GSp_{2n} \times GL_1$ and algebraicity
of symmetric fourth $L$-values for $GL_2$Pitale A Saha A Schmidt R
Annales MathéMatiques Du QuéBec, Springer (Part of Springer Nature)
06-05-2020
2019
Sup-norms of eigenfunctions in the level aspect for compact arithmetic
surfacesSaha A
Mathematische Annalen, Springer (Part of Springer Nature)
01-11-2019
On the order of vanishing of newforms at cuspsCorbett A Saha A
Mathematical Research Letters, International Press vol. 25 (6), 1771-1804.
25-03-2019
2017
On sup-norms of cusp forms of powerful levelSaha A
Journal of The European Mathematical Society, European Mathematical Society vol. 19 (11)
01-11-2017
A note on the growth of nearly holomorphic vector-valued Siegel modular formsPitale A SAHA A Schmidt R
Contributions in Mathematical and Computational Sciences
16-10-2017
Hybrid sup-norm bounds for Maass newforms of powerful levelSaha A
Algebra and Number Theory, Mathematical Sciences Publishers vol. 11 (5), 1009-1045.
12-07-2017
Local and global Maass relationsPitale A Saha A Schmidt R
Mathematische Zeitschrift, Springer Verlag vol. 287 (1-2), 655-677.
09-01-2017
2015
Large Values of Newforms on GL(2) with Highly Ramified Central CharacterSaha A
International Mathematics Research Notices vol. 2016 (13), 4103-4131.
01-10-2015
Representations of SL_2(R) and nearly holomorphic modular formsPitale A Saha A Schmidt R
03-01-2015
2014
Transfer of Siegel cusp forms of degree 2Pitale A Saha A Schmidt R
Memoirs of The American Mathematical Society, American Mathematical Society vol. 232 (1090)
01-11-2014
2013
Bounds for Rankin--Selberg integrals and quantum unique ergodicity for
powerful levelsNelson PD Pitale A Saha A
Journal of The American Mathematical Society, American Mathematical Society
06-08-2013
A relation between multiplicity one and Bocherer's conjectureSaha A
The Ramanujan Journal, Springer Verlag
02-07-2013
Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L
-functionsSaha A Schmidt R
Journal of The London Mathematical Society, Wiley vol. 88 (1), 251-270.
18-04-2013
On ratios of Petersson norms for Yoshida liftsSaha A
21-03-2013
Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functionsSaha A Schmidt R
In Arxiv
22-01-2013
2012
Determination of modular forms by fundamental Fourier coefficientsSaha A
30-07-2012
Local spectral equidistribution for Siegel modular forms and applicationsKowalski E Saha A Tsimerman J
Compositio Mathematica, Cambridge University Press (Cup) vol. 148 (2), 335-384.
21-02-2012
2011
Siegel cusp forms of degree 2 are determined by their fundamental
Fourier coefficientsSaha A
25-06-2011
2010
Prime density results for Hecke eigenvalues of a Siegel cusp formSaha A
27-07-2010
2009
Pullbacks of Eisenstein series from GU(3,3) and critical L-values for
GSp(4) X GL(2)Saha A
26-04-2009
L-Functions for Holomorphic Forms on GSp(4) x GL(2) and Their Special ValuesSaha A
International Mathematics Research Notices
13-02-2009
2008
Hilbert modular forms of weight 1/2 and theta functionsAchimescu S Saha A
Journal of Number Theory, Elsevier Bv vol. 128 (12), 3037-3062.
01-12-2008
Explicit refinements of Böcherer's conjecture for Siegel modular forms
of squarefree levelDickson M Pitale A Saha A Schmidt R
Journal of The Mathematical Society of Japan, Mathematical Society of Japan
Lowest weight modules of Sp_4(R) and nearly holomorphic Siegel modular
formsPitale A Saha A Schmidt R
Kyoto Journal of Mathematics, Duke University Press
Some analytic aspects of automorphic forms on GL(2) of minimal typeHu Y Nelson PD Saha A
Commentarii Mathematici Helvetici, European Mathematical Society vol. 94 (4), 767-801.
Integrality and cuspidality of pullbacks of nearly holomorphic Siegel
Eisenstein seriesPitale A Saha A Schmidt R
Publicacions Matematiques, Universitat De Barcelona
On fundamental Fourier coefficients of Siegel cusp forms of degree 2Jääsaari J Lester S Saha A
Journal of The Institute of Mathematics of Jussieu, Cambridge University Press (Cup)
Grants
Grants of specific relevance to the Centre for Combinatorics, Algebra and Number TheoryFourier coefficients, periods and L-functionsAbhishek Saha
£75,827 Engineering and Physical Sciences Research Council
18-12-2024 - 17-01-2026
Automorphic Forms and L-Functions of Higher Rank WorkshopAbhishek Saha
£3,000 London Mathematical Society (LMS)
01-09-2023 - 30-09-2023
EPSRC Small Grant - New bounds towards Fourier coefficients of Siegel modular formsAbhishek Saha
£80,624 EPSRC Engineering and Physical Sciences Research Council
01-11-2021 - 31-07-2022
Automorphic Forms On Higher Rank Groups: Fourier Coefficients, L-functions, and arithmeticAbhishek Saha and Stephen Lester
£388,041 EPSRC Engineering and Physical Sciences Research Council
15-06-2020 - 14-12-2023
New investigations in automorphic formsAbhishek Saha
£293,684 Leverhulme Trust
01-09-2019 - 31-05-2024
Collaborative research with Professor A. Pitale , USAAbhishek Saha
£1,000 London Mathematical Society (LMS)
01-06-2019 - 30-06-2019
Research Group
PhD Students
- Kuba Dobrowolski
Moments of The Central L-Values on Higher Rank Groups - James Kiln
Deformations of Galois Representations and Congruences Between Modular Forms
News
No news items found.