Research
Research
Research
Research
748+ open-access research outputs.
Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $\alpha \in \mathcal{OP}_n$, let $F(\alpha)=\{y\in X_n: y\alph…
Let $G=PSL(n,\mathbb{C})$. Let $T$ be a maximal torus of $G$. Let $\omega_{r}$ denote the $r^{th}$ fundamental weight. Let $\mathcal{L}(n\omega_{r})$ denote the line bundle on the Grassmannian $G_{r,n…
We develop a unified T-extended framework for weakly contractive, weakly Kannan, and Geraghty classes of self-maps S on a metric space (X, d), where distances are measured on the auxiliary image via d…
We prove that for any pair of irreducible principal series representations $(\pi_1,\pi_2)$ of $\operatorname{GL}_n(\mathbb{R})$ in general position, the notions of exceptional pole of type 1 and type …
For a simple graph $G$ with $n$ vertices, let $A_G$ denote the adjacency matrix of $G$, and let $\lambda_1(G) \geq \lambda_2(G) \geq \dots \geq \lambda_n(G)$ be its eigenvalues. For an integer $p \geq…
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise …
We prove an asymptotic formula for the second moment of the first derivative of quadratic twists of modular $L$-functions with three leading order main terms. It improves the previous result of Kumar …
The modular forms and weighted densities over the 1-dimensional manifold $M$ are transformed ``alike" under the group of linear fractional changes of coordinates, so the classifications of differentia…
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes betwee…
Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-\beta_j)$, $|\beta_j|>1$ for …
The coefficients $A_n(\alpha,\beta,\omega)$ in the Maclaurin expansion $(1+\omega z)^{\alpha}(1-z)^{-\beta}= \sum_{n=0}^{\infty} A_n(\alpha,\beta,\omega)z^n$ are studied, where $\omega,z \in \mathbb{C…
In this paper, we study inequalities involving polynomials and quasimodular forms. More precisely, we focus on the monotonicity of the functions of the form $t \mapsto t^m F(it)$ where $F$ is a quasim…
The Orbit Problem asks whether the orbit of a point under a matrix reaches a given target set. When the target is a single point, the problem was shown to be decidable in polynomial time by Kannan and…
The Rankin--Cohen brackets provide a basic example of ``non-elementary" differential symmetry breaking operators. They can be interpreted as bi-differential operators remarkable for reflecting the str…
In 2021, Henk, Schymura and Xue introduced packing minima, associated with a convex body and a lattice, as packing counterparts to the covering minima of Kannan and Lov\'asz. Motivated by conjectures …
In this paper, we explore the relationship between Rankin-Cohen brackets for vector-valued modular forms and Petersson's inner products, deriving an explicit description of the adjoint map for the bra…
For any modulus of continuity $\omega$ that fails the Osgood condition, we construct a divergence-free velocity field $v \in C_t C^\omega_x$ for which the associated ODE admits at least two distinct f…
While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this …
As a consequence of the Littlewood-Richardson (LR) commuters coincidence and the Kumar-Torres branching model via Kushwaha-Raghavan-Viswanath flagged hives, we have solved the Lecouvey- -Lenart conjec…
We establish standard zero-free regions with no exceptional Landau-Siegel zeros for Rankin-Selberg $L$-functions and triple product $L$-functions in several new families for which modularity is not ye…
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