skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Feng, Tony"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Geometric and Functional Analysis)
    Abstract We study conjectures of Ben-Zvi–Sakellaridis–Venkatesh that categorify the relationship between automorphic periods andL-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method. 
    more » « less
    Free, publicly-accessible full text available April 1, 2026
  2. ; ; ; ; (, Compositio Mathematica)
    Let$$G$$be a split semisimple group over a global function field$$K$$. Given a cuspidal automorphic representation$$\Pi$$of$$G$$satisfying a technical hypothesis, we prove that for almost all primes$$\ell$$, there is a cyclic base change lifting of$$\Pi$$along any$$\mathbb {Z}/\ell \mathbb {Z}$$-extension of$$K$$. Our proof does not rely on any trace formulas; instead it is based on using modularity lifting theorems, together with a Smith theory argument, to obtain base change for residual representations. As an application, we also prove that for any split semisimple group$$G$$over a local function field$$F$$, and almost all primes$$\ell$$, any irreducible admissible representation of$$G(F)$$admits a base change along any$$\mathbb {Z}/\ell \mathbb {Z}$$-extension of$$F$$. Finally, we characterize local base change more explicitly for a class of toral representations considered in work of Chan and Oi. 
    more » « less
    Full Text Available 
  3. ; ; (, Inventiones mathematicae)
    Abstract We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the$$r^{\mathrm{th}}$$ r th central derivative of non-singular Fourier coefficients of a normalized Siegel–Eisenstein series, and (2) the degree of special cycles of “virtual dimension 0” on the moduli stack of hermitian shtukas with$$r$$ r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series. 
    more » « less
    Full Text Available 
  4. ; ; (, Notices of the International Consortium of Chinese Mathematicians)
    Full Text Available 
  5. ; ; (, Mathematische Annalen)
    Abstract Fix a positive integernand a finite field$${\mathbb {F}}_q$$ F q . We study the joint distribution of the rank$${{\,\mathrm{rk}\,}}(E)$$ rk ( E ) , then-Selmer group$$\text {Sel}_n(E)$$ Sel n ( E ) , and then-torsion in the Tate–Shafarevich group Equation missing<#comment/>asEvaries over elliptic curves of fixed height$$d \ge 2$$ d ≥ 2 over$${\mathbb {F}}_q(t)$$ F q ( t ) . We compute this joint distribution in the largeqlimit. We also show that the “largeq, then large height” limit of this distribution agrees with the one predicted by Bhargava–Kane–Lenstra–Poonen–Rains. 
    more » « less