Browsing School of Mathematical Sciences by Author "Saha, A"
Now showing items 1-18 of 18
-
Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels
Nelson, PD; Pitale, A; Saha, A (American Mathematical Society, 2014-01-01)Let f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infinity. This generalizes known results in the ... -
Equality, Diversity and Inclusion in the Mathematics Community: A Perspective on Data and Policy
Saha, A (Cambridge University Press, 2024-06-04)Equality, Diversity and Inclusion (EDI) questions have taken on increasing importance within the mathematics community recently and generated substantial debate. This article focuses on data collection, data analysis and ... -
Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level
Dickson, M; Pitale, A; Saha, A; Schmidt, RWe formulate an explicit refinement of B\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve ... -
Hybrid sup-norm bounds for Maass newforms of powerful level
Saha, A (Mathematical Sciences Publishers, 2017-07-12)Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer ... -
Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series
Pitale, A; Saha, A; Schmidt, RWe study nearly holomorphic Siegel Eisenstein series of general levels and characters on $\mathbb{H}_{2n}$, the Siegel upper half space of degree $2n$. We prove that the Fourier coefficients of these Eisenstein series (once ... -
Local and global Maass relations
Pitale, A; Saha, A; Schmidt, R (Springer Verlag, 2017-10-01)We characterize the irreducible, admissible, spherical representations of GSp(4,F) (where F is a p-adic field) that occur in certain CAP representations in terms of relations satisfied by their spherical vector in a special ... -
Lowest weight modules of Sp_4(R) and nearly holomorphic Siegel modular forms
Pitale, A; Saha, A; Schmidt, RWe undertake a detailed study of the lowest weight modules for the Hermitian symmetric pair (G,K), where G=Sp_4(R) and K is its maximal compact subgroup. In particular, we determine K-types and composition series, and write ... -
The Manin constant and the modular degree
Cesnavicius, K; Neururer, M; Saha, AThe Manin constant $c$ of an elliptic curve $E$ over $\mathbb{Q}$ is the nonzero integer that scales the pullback of a N\'{e}ron differential under a minimal parametrization $\phi\colon X_0(N)_{\mathbb{Q}} \twoheadrightarrow ... -
On Fourier Coefficients and Hecke Eigenvalues of Siegel Cusp Forms of Degree 2
Paul, B; Saha, A (2022) -
On fundamental Fourier coefficients of Siegel cusp forms of degree 2
Jääsaari, J; Lester, S; Saha, A (Cambridge University Press (CUP), 2021)Let $F$ be a Siegel cusp form of degree 2, even weight $k \geq 2$ and odd squarefree level $N$. We undertake a detailed study of the analytic properties of Fourier coefficients $a(F,S)$ of $F$ at fundamental matrices $S$ ... -
On sup-norms of cusp forms of powerful level
Saha, A (European Mathematical Society, 2017-11-01)Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty <<_{\lambda, \epsilon} N^{-1/12 + \epsilon} for any \epsilon>0. The exponent is further improved ... -
On the order of vanishing of newforms at cusps
Corbett, A; Saha, ALet $E$ be an elliptic curve over $\mathbb{Q}$ of conductor $N$. We obtain an explicit formula, as a product of local terms, for the ramification index at each cusp of a modular parametrization of $E$ by $X_0(N)$. Our ... -
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 (Springer (part of Springer Nature), 2020)We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree ... -
A relation between multiplicity one and Bocherer's conjecture
Saha, AWe show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2. -
Some analytic aspects of automorphic forms on GL(2) of minimal type
Hu, Y; Nelson, PD; Saha, ALet $\pi$ be a cuspidal automorphic representation of $PGL_2(\mathbb{A}_\mathbb{Q})$ of arithmetic conductor $C$ and archimedean parameter $T$, and let $\phi$ be an $L^2$-normalized automorphic form in the space of $\pi$. ... -
THE SPECIAL VALUES OF THE STANDARD <i>L</i>-FUNCTIONS FOR GSp<sub>2<i>n</i></sub> x GL<sub>1</sub>
Horinaga, S; Pitale, A; Saha, A; Schmidt, R (2022) -
Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces
Saha, A (Springer (part of Springer Nature), 2019-11-01)Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic ... -
Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity
Hu, Y; Saha, AWe improve upon the local bound in the depth aspect for sup-norms of newforms on $D^\times$ where $D$ is an indefinite quaternion division algebra over $\Q$. Our sup-norm bound implies a depth-aspect subconvexity bound for ...