6 papers
Rank 2 Affine Invariant Subvarieties in H(6)
Pramana Saldin, Ruocheng Yang
We classify rank 2 rel 0 arithmetic affine invariant subvarieties in the minimal stratum H(6). The proof follows and extends Apisa's approach in genus three, reducing the analysis…
Classification of Finite Groups With Equal Left and Right Quotient Sets
Haran Mouli, Pramana Saldin
In this paper, we classify all finite groups which have the following property: for all subsets , we have . This question is motivated by…
Centered Moments of Weighted One-Level Densities of -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 -functions is well-modeled by the behavior of eigenvalues near of some classic…
Comparing Left and Right Quotient Sets in Groups
Julian Duvivier, Xiaoyao Huang, Ava Kennon +5
For a finite subset of a group , we define the right quotient set and the left quotient set of , respectively, as , $A^{-1}A := \…
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 -functions ordered by analytic conductor converge, as , to the…
Finite-State Machines for Horospheres in Hyperbolic Right-Angled Coxeter Groups
Noah Jillson, Daniel N. Levitin, Pramana Saldin +3
Relatively little is known about the discrete horospheres in hyperbolic groups, even in simple settings. In this paper we work with hyperbolic one-ended right-angled Coxeter groups…