V. Muthuvel

activity

20232026

collaborators

5 papers

math.NT2026

Inducing Whittaker Functions from Higher Ranks

Vishal Muthuvel

We construct a family of Whittaker functions for $S L (m, Z)$ induced directly from Whittaker functions for $S L (n, Z)$ , for any $2 \leq m < n$ . Given Jacquet's Whittake…

math.NT2026

Explicit Formulas for the Casimir Eigenvalues of $S L (n, Z)$ -Maass Forms

Vishal Muthuvel

Maass forms for $S L (n, Z)$ are defined to be eigenfunctions of the Casimir operators $D_{m, n}$ of orders $1 \leq m \leq n$ for $G L (n, R)$ . For any $1 \leq…

math.NT2025

Centered Moments of Weighted One-Level Densities of $G L (2)$ $L$ -Functions

Lawrence Dillon, Xiaoyao Huang, Say-Yeon Kwon +6

Katz and Sarnak conjectured that the behavior of zeros near the central point of any family of $L$ -functions is well-modeled by the behavior of eigenvalues near $1$ of some classic…

math.NT2025

Breaking Universality in the Lower Order Terms in the 1-level and 2-level Density of Holomorphic Cusp Newforms

Yuval Amit, Lawrence Dillon, Lucas Chen +12

The Katz--Sarnak density conjecture predicts that the normalized low-lying zeros of a family of $L$ -functions ordered by analytic conductor $R$ converge, as $R \to \infty$ , to the…

math.AC2023

Units of hyperelliptic curves over $F_{2}$

Justin Chen, Vishal Muthuvel

We study unit groups of rings of the form $F_{2} [x, y] / (y^{2} + g y + h)$ , for $g, h \in F_{2} [x]$ -- in particular, the question of (non)triviality of such unit groups.…

Inducing Whittaker Functions from Higher Ranks

Explicit Formulas for the Casimir Eigenvalues of SL(n,Z)-Maass Forms

Centered Moments of Weighted One-Level Densities of GL(2) L-Functions

Breaking Universality in the Lower Order Terms in the 1-level and 2-level Density of Holomorphic Cusp Newforms

Units of hyperelliptic curves over F2​

Explicit Formulas for the Casimir Eigenvalues of $S L (n, Z)$ -Maass Forms

Centered Moments of Weighted One-Level Densities of $G L (2)$ $L$ -Functions

Units of hyperelliptic curves over $F_{2}$