Pramana Saldin

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20242026

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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

Comparing Left and Right Quotient Sets in Groups

Julian Duvivier, Xiaoyao Huang, Ava Kennon +5

For a finite subset $A$ of a group $G$ , we define the right quotient set and the left quotient set of $A$ , respectively, as $A A^{- 1} := {a_{1} a_{2}^{- 1} : a_{1}, a_{2} \in A}$ , $A^{-1}A := \…

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…

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

Comparing Left and Right Quotient Sets in Groups

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

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