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pro vyhledávání: '"vaishya, Lalit"'
Autor:
Pandey, Manish Kumar, vaishya, Lalit
In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; \begin{equation*}
Externí odkaz:
http://arxiv.org/abs/2401.18055
Autor:
Charan, Mrityunjoy, Vaishya, Lalit
In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with
Externí odkaz:
http://arxiv.org/abs/2401.02182
Autor:
Vaishya, Lalit
In the article, we investigate the average behaviour of normalised Hecke eigenvalues over certain polynomials and establish an estimate for the power moments of the normalised Hecke eigenvalues of a normalised Hecke eigenform of weight $k \ge 2$ for
Externí odkaz:
http://arxiv.org/abs/2308.12953
Let $f \in S_{k}(SL_2(\mathbb{Z}))$ be a normalized Hecke eigenforms of integral weight $k$ for the full modular group. In the article, we study the average behaviour of Fourier coefficients of $\ell$-fold product $L$-function. More precisely, we est
Externí odkaz:
http://arxiv.org/abs/2307.13439
Autor:
Roy, Bidisha, Vaishya, Lalit
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along with cert
Externí odkaz:
http://arxiv.org/abs/2304.09003
Autor:
Ramakrishnan, B., Vaishya, Lalit
In this article, we consider the problem of determining formulas for the number of representations of a natural number $n$ by a sum of figurate numbers with certain positive integer coefficients. To achieve this, we prove that the associated generati
Externí odkaz:
http://arxiv.org/abs/2302.00964
Autor:
Jha, Abash Kumar, Vaishya, Lalit
In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.
Comment: to appear in Functiones et Approximatio Commentarii Mathematici (2022)
Comment: to appear in Functiones et Approximatio Commentarii Mathematici (2022)
Externí odkaz:
http://arxiv.org/abs/2206.07742
Autor:
Vaishya, Lalit
In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant $D < 0$ wh
Externí odkaz:
http://arxiv.org/abs/2204.08310
Autor:
Ramakrishnan, B., Vaishya, Lalit
In \cite{ono}, K. Ono, S. Robins and P.T. Wahl considered the problem of determining formulas for the number of representations of a natural number $n$ by a sum of $k$ triangular numbers and derived many applications, including the one connecting the
Externí odkaz:
http://arxiv.org/abs/1904.06369
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