Searcharxiv⌕ Search

arXiv subjects

Miao Pam Gu

Publications and source records attributed to Miao Pam Gu.

6 recordsLinked to original sources
arXiv2026

On triple product $L$-functions and the fiber bundle method

We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product $L$-function times a product of $L$-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show how it implies the analytic properties of triple product $L$-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a simpler case of the Poisson summation conjecture along with certain local compatibility statements.

math.NT↗
arXiv2026

Kloosterman sheaves and Bessel functions for generic principal series of finite groups

Let $G$ be a quasi-split reductive group over a finite field and let $Ĝ$ be the Langlands dual group. Assuming the derived subgroup of $G$ is almost simple, we use techniques from the geometric Langlands program to relate special values of Bessel functions for generic principal series representations of $G$ to the trace of Frobenius acting on Kloosterman sheaves of Heinloth-Ngô-Yun for $Ĝ$. We also give explicit examples in essentially all possible cases, including exceptional groups.

math.RT↗
arXiv2026

Plancherel and Poisson summation formulae for a family of affine $Ψ$-bundles

We prove a Plancherel formula for a family of affine $Ψ$-bundles. As an application, we construct Fourier transforms and asymptotic Schwartz spaces for the family. We then prove the corresponding Poisson summation formula under suitable assumptions. The choice of affine $Ψ$-bundles we consider is motivated by applications to triple product $L$-functions explored in another paper of the authors and Leslie.

math.NT↗
arXiv2024

Euler characteristics of the generalized Kloosterman sheaves for symplectic and orthogonal groups

We study the monodromy of certain $\ell$-adic local systems attached to the generalized Kloosterman sheaves constructed by Yun and calculate their Euler characteristics under standard representations in the cases of symplectic and split/quasi-split orthogonal groups. This provides evidence for the conjectural description of their Swan conductors at $\infty$ which is predicted by Reeder-Yu on the Langlands parameters attached to the epipelagic representations.

math.NT↗
arXiv2023

Conics meeting eight lines over perfect fields

Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-space. Using the Euler class and local degree from motivic homotopy theory, we give an enriched version of this result over any perfect field. This provides a weighted count of the number of plane conics meeting 8 general lines, where the weight of each conic is determined the geometry of its intersections with the 8 given lines. As a corollary, real conics meeting 8 general lines come in two families of equal size.

math.AG↗