Zobrazeno 1 - 10
of 249
pro vyhledávání: '"Singh, Anup Kumar"'
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:
Rangan, N. Mohan1 (AUTHOR), Singh, Anup Kumar1 (AUTHOR), Yadav, Rekha C.1 (AUTHOR) rekha.pt@rediffmail.com, Roy, Indranil Deb1 (AUTHOR), Tomar, Kapil1 (AUTHOR), Singh, Neha2 (AUTHOR), R, Vasanthanarayanan1 (AUTHOR)
Publikováno v:
Journal of Rare Diseases. 10/9/2024, Vol. 3 Issue 1, p1-10. 10p.
Autor:
Bhol, Nitish Kumar, Bhanjadeo, Madhabi Madhusmita, Singh, Anup Kumar, Dash, Umesh Chandra, Ojha, Rakesh Ranjan, Majhi, Sanatan, Duttaroy, Asim K., Jena, Atala Bihari
Publikováno v:
In Biomedicine & Pharmacotherapy September 2024 178
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:
Kumari, Priya, Sharma, Juhi, Singh, Anup Kumar, Pandey, Ajay Kumar, Yusuf, Farnaz, Kumar, Shashi, Gaur, Naseem A.
Publikováno v:
In Chemical Engineering Journal 1 February 2023 453 Part 2
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
Autor:
Singh, Anup Kumar1 (AUTHOR), Deeba, Farha1 (AUTHOR), Kumar, Mohit1 (AUTHOR), Kumari, Sonam1,2 (AUTHOR), Wani, Shahid Ali1 (AUTHOR), Paul, Tanushree1 (AUTHOR), Gaur, Naseem A.1 (AUTHOR) naseem@icgeb.res.in
Publikováno v:
Microbial Cell Factories. 10/6/2023, Vol. 22 Issue 1, p1-16. 16p.
Autor:
Singh, Anup Kumar1,2,3 (AUTHOR) ak.singh@ncl.res.in, Swain, Gitanjali1,2 (AUTHOR)
Publikováno v:
ChemistrySelect. 8/4/2023, Vol. 8 Issue 29, p1-9. 9p.
In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.
Comment: 20 pa
Comment: 20 pa
Externí odkaz:
http://arxiv.org/abs/1708.04266
In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the formulas
Externí odkaz:
http://arxiv.org/abs/1702.01249