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    AuthorSaha, A (14)Pitale, A (6)Schmidt, R (5)Hu, Y (2)Nelson, PD (2)Corbett, A (1)Dickson, M (1)Horinaga, S (1)Jääsaari, J (1)Lester, S (1)Subject
    math.NT (14)
    math.RT (2)math.SP (2)11F11 (Primary) 11F70, 22E50, 58J51 (Secondary) (1)math.DS (1)... View MoreDate Issued2021 (1)2020 (1)2019 (1)2017 (3)2014 (1)
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    Some analytic aspects of automorphic forms on GL(2) of minimal type 

    Hu, Y; Nelson, PD; Saha, A
    Let $\pi$ 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 $\pi$. ...
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    Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level 

    Dickson, M; Pitale, A; Saha, A; Schmidt, R
    We 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 ...
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    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 ...
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    On the order of vanishing of newforms at cusps 

    Corbett, A; Saha, A
    Let $E$ 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 ...
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    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 ...
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    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 ...
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    A relation between multiplicity one and Bocherer's conjecture 

    Saha, A
    We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.
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    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 ...
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    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 ...
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    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 ...
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