Haonan Gu

collaborators

4 papers

math.NT2025

Expository notes on Spectral Reciprocity with Explicit Transform

Haonan Gu

We assemble three basic analytic inputs -- the Kuznetsov trace formula on $SL_{2} (Z)$ with explicit continuous spectrum, the $GL_{3}$ Voronoi formula, and $t$ …

math.NA2025

The Instability of PainlevÃ© Equations in Recovering Largest Eigenvalue Distributions of GUE, LUE, JUE and an Attempt of Solution to It

Haonan Gu

The distribution of the largest eigenvalue for the three classical unitary ensembles -- GUE, LUE, and JUE -- admits two complementary exact descriptions: (i) as Fredholm determinan…

math.NT2025

Towards a finite-slope universal Rankin-Selberg p-adic L-function

Haonan Gu

This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$ -adic $L$ -functions in universal deformation families. Starting from resi…

math.GM2025

P-adic integrals: A solution to the p-adic Schrodinger Equation

Haonan Gu

This paper first introduces the concept of p-adic number and field. Then it develops the p-adic integration and applied it to solve p-adic Schrodinger equations.