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pro vyhledávání: '"Ramakrishnan, B."'
If $f(z)$ is a modular form of weight $k$, then the differential operator $\vartheta_k$ defined by $\vartheta_k(f) = \frac{1}{2\pi i} \frac{d}{dz}f(z) - \frac{k}{12} E_2(z) f(z)$ (known as the Ramanujan-Serre derivative map) is a modular form of weig
Externí odkaz:
http://arxiv.org/abs/2303.02921
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
Publikováno v:
In Engineering Applications of Artificial Intelligence December 2024 138 Part A
In this paper, we consider the following diagonal quadratic forms \begin{equation*} a_1x_1^2 + a_2x_2^2 + \cdots + a_{\ell}x_{\ell}^2, \end{equation*} where $\ell\ge 5$ is an odd integer and $a_i\ge 1$ are integers. By using the extended Shimura corr
Externí odkaz:
http://arxiv.org/abs/2110.03974
Autor:
Varghese, Edna Mary, Kour, Babanpreet, Ramya, S., Krishna, Pooja D., Nazla, K.A., Sudheer, K., Anith, K.N., Jisha, M.S., Ramakrishnan, B.
Publikováno v:
In Applied Soil Ecology April 2024 196
Publikováno v:
In Current Research in Microbial Sciences 2024 6
Autor:
Das, Sujit, Biswas, Sunanda, Ramakrishnan, B., Das, T.K., Purakayastha, T.J., Gawade, B.H., Singh, Priya, Ghorai, Partha Sarathi, Tripathy, Saloni, Sinha, Kanchan
Publikováno v:
In Applied Soil Ecology January 2024 193
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
In this paper, we find a basis for the space of modular forms of weight $2$ on $\Gamma_1(48)$. We use this basis to find formulas for the number of representations of a positive integer $n$ by certain quaternary quadratic forms of the form $\sum_{i=1
Externí odkaz:
http://arxiv.org/abs/1801.04392