Professor Abhishek Saha
Professor of Mathematics, Deputy Director of Research
Email: abhishek.saha@qmul.ac.ukTelephone: +44 (0)20 7882 3914Room Number: Mathematical Sciences Building, Room: MB-514Website: http://www.maths.qmul.ac.uk/~asaha/ Office Hours: Please email for an appointment
Profile
Research
Research Interests:
Abhishek Saha's research interests include number theory, automorphic forms, classical and higher rank modular forms, representations of p-adic groups, automorphic representations, and L-functions. Broadly speaking, his current research has two main directions. One direction deals with the analytic properties of automorphic forms and their associated L-functions. The other direction investigates the arithmetic and algebraic properties of cohomological automorphic representations, especially those coming from classical or Siegel modular forms. Thus, Saha straddles a uniquely broad research portfolio, with expertise in the areas of modular forms, algebraic number theory, modern representation theoretic methods, as well as techniques of analytic number theory.
For a full list of his publications, click here.
Saha's research group currently includes three PDRAs: Han Wu, Jesse Jaasaari, and Biplab Paul as well as three PhD students: Félicien Comtat, Tim Davis, and Osmundur Justinussen.
Publications
- (2022), Integrality And Cuspidality Of Pullbacks Of Nearly Holomorphic Siegel Eisenstein Series Publicacions Matematiques $nameOfConference(2021), Lowest weight modules of Sp
4 (R) and nearly holomorphic Siegel modular forms Kyoto Journal of Mathematics $nameOfConference(2021), The special values of the standard $L$-functions for $\mathrm{GSp}_{2n} \times \mathrm{GL}_1$ $journal $nameOfConference(2021), ON FUNDAMENTAL FOURIER COEFFICIENTS of SIEGEL CUSP FORMS of DEGREE 2 Journal of the Institute of Mathematics of Jussieu $nameOfConference(2020), Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity Compositio Mathematica $nameOfConference(publicationYear), On the standard $L$-function for $GSp_{2n} \times GL_1$ and algebraicity of symmetric fourth $L$-values for $GL_2$ Annales mathématiques du Québec $nameOfConference(2020), Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level Journal of the Mathematical Society of Japan $nameOfConference(2019), The Manin constant and the modular degree $journal $nameOfConference(2019), Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces Mathematische Annalen $nameOfConference(2019), On the order of vanishing of newforms at cusps Mathematical Research Letters $nameOfConference(2019), Some analytic aspects of automorphic forms on GL(2) of minimal type Commentarii Mathematici Helvetici $nameOfConference(2017), On sup-norms of cusp forms of powerful level Journal of the European Mathematical Society $nameOfConference(2017), A note on the growth of nearly holomorphic vector-valued Siegel modular forms Contributions in Mathematical and Computational Sciences $nameOfConference(2017), Hybrid sup-norm bounds for Maass newforms of powerful level Algebra and Number Theory $nameOfConference(2017), Local and global Maass relations Mathematische Zeitschrift $nameOfConference(2016), Large Values of Newforms on GL(2) with Highly Ramified Central Character International Mathematics Research Notices $nameOfConference(2015), Representations of SL_2(R) and nearly holomorphic modular forms $journal $nameOfConference(2014), Transfer of Siegel cusp forms of degree 2 Memoirs of the American Mathematical Society $nameOfConference(2014), Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels Journal of the American Mathematical Society $nameOfConference(publicationYear), A relation between multiplicity one and Bocherer's conjecture The Ramanujan Journal $nameOfConference(2013), Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L -functions Journal of the London Mathematical Society $nameOfConference(2013), On ratios of Petersson norms for Yoshida lifts $journal $nameOfConference(2012), Determination of modular forms by fundamental Fourier coefficients $journal $nameOfConference(2012), Local spectral equidistribution for Siegel modular forms and applications Compositio Mathematica $nameOfConference(2011), Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients $journal $nameOfConference(2010), Prime density results for Hecke eigenvalues of a Siegel cusp form $journal $nameOfConference(2009), Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2) $journal $nameOfConference(publicationYear), L-Functions for Holomorphic Forms on GSp(4) x GL(2) and Their Special Values International Mathematics Research Notices $nameOfConference(2008), Hilbert modular forms of weight 1/2 and theta functions Journal of Number Theory $nameOfConference