2 citations · 3 across the 8 of their papers we have counts for
8 papers
Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures
Debmalya Basak, Anji Dong, Katerina Saettone +1
On the occasion of George Andrews' and Bruce Berndt's combined 170th birthday, we prove two conjectures of Sir Frederick Pollock that are more than 170 years old. In 1843, Pollock…
A Conditional Refinement of Page's Theorem on zeros of Dirichlet -functions
Debmalya Basak, Kyle Pratt
Landau--Siegel zeros are hypothetical zeros of Dirichlet -functions that are close to the point . A classic theorem of Page shows at most one such zero can exist among all…
An Analogue of the Dedekind Eta Function for Hecke Groups
Debmalya Basak, Dorian Goldfeld, Winston Heap +2
Let be a fundamental discriminant of a real quadratic field. We construct an analogue of the classical Dedekind eta function for the Hecke group .…
Almost all primes are not needed in Ternary Goldbach
Debmalya Basak, Raghavendra N. Bhat, Anji Dong +1
The ternary Goldbach conjecture states that every odd number can be written as the sum of three primes. We construct a set of primes defined by an expa…
Non-vanishing and One Level Density for Dirichlet -functions Along Short Averages
Debmalya Basak
Assuming the Generalized Riemann Hypothesis, it is known that at least half of the central values are non-vanishing as ranges over primitive characters modul…
Remarks on Landau-Siegel zeros
Debmalya Basak, Jesse Thorner, Alexandru Zaharescu
For certain families of -functions, we prove that if each -function in the family has only real zeros in a fixed yet arbitrarily small neighborhood of , then one may con…
Exponential sums over Möbius convolutions with applications to partitions
Debmalya Basak, Nicolas Robles, Alexandru Zaharescu
We consider partitions of a positive integer arising from the generating functions \[ \sum_{n=1}^\infty p_{w}(n) z^n = \prod_{m \in \mathbb{N}} (1-z^m)^{-w(m)}, \] w…
The asymptotic properties of and a problem related to visibility of Lattice points
Debmalya Basak
We look at the average sum of the Euler's phi function and it's relation with the visibility of a point from the origin.We show that $\forall{\hspace{0.05in}{k} \ge{1}},k\…