arXiv subjects

Pranjal Vishwakarma

Publications and source records attributed to Pranjal Vishwakarma.

2 recordsLinked to original sources

arXiv2025

An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus

We describe an algorithmic method to determine the image of restriction maps for Siegel modular forms with \textit{arbitrary} characters and arbitrary weight. A program has been implemented in the mathematical software \texttt{Java} to compute the Fourier expansion of the image of these restriction maps for Siegel modular forms of genus two. This approach allows us to compute an upper bound for the space of Siegel modular forms with {\it non-trivial} character (which has not been previously known) and arbitrary weights (including low weight $k \leq 4$).

math.NT↗

arXiv2024

Two results on Eisenstein part of homology and cohomology groups of Bianchi modular groups

We explicitly write down the {\it Eisenstein cycles} in the first homology groups of quotients of the hyperbolic three spaces as linear combinations of Cremona symbols (a generalization of Manin symbols) for imaginary quadratic fields. They generate the Eisenstein part of the homology groups. We also study the Eisenstein part of the cohomology groups. As an application, we find an asymptotic dimension formula (level aspect) for the cuspidal cohomology groups of congruence subgroups of the form $\Ga_1(N)$ inside the full {\it Bianchi groups}.

math.NT↗