4 citations · 4 across the 6 of their papers we have counts for
6 papers
First Derivative of Automorphic Function of Triangle Groups
Md. Shafiul Alam, Bijan Krishna Saha, Chinmayee Podder
For a triangle group , the -automorphic function is the inverse of Schwarz triangle function. In this paper, we compute the first derivative of the -automorphic function f…
Automorphic Forms and Holomorphic Functions on the Upper Half-plane
Md. Shafiul Alam
We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also…
Geometric deduction of the solutions to modular equations
Md. Shafiul Alam, Toshiyuki Sugawa
In his notebooks, Ramanujan presented without proof many remarkable formulae for the solutions to generalized modular equations. Much later, proofs of the formulae were provided by…
On Ramanujan's Modular Equations and Hecke Groups
Md. Shafiul Alam
Inspired by the work of S. Ramanujan, many people have studied generalized modular equations and the numerous identities found by Ramanujan. These identities known as modular equat…
Improved upper and lower bounds for the point placement problem
Md. Shafiul Alam, Asish Mukhopadhyay
The point placement problem is to determine the positions of a set of distinct points, P = {p1, p2, p3, ..., pn}, on a line uniquely, up to translation and reflection, from the…
Algorithms for the Problems of Length-Constrained Heaviest Segments
Md. Shafiul Alam, Asish Mukhopadhyay
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segment…