50 citations · 222 across the 52 of their papers we have counts for
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Modularity of higher theta series I: cohomology of the generic fiber
Tony Feng, Zhiwei Yun, Wei Zhang
In a previous paper we constructed higher theta series for unitary groups over function fields, and conjectured their modularity properties. Here we prove the generic modularity of…
Rigidity method for automorphic forms over function fields
Zhiwei Yun
These are lectures given at the 2022 Arizona Winter School. It gives an introduction to the rigidity method for constructing automorphic forms for semisimple groups over function f…
Automorphic Forms on Unitary Groups
Ellen Eischen
This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond . The main focus of th…
Higher theta series for unitary groups over function fields
Tony Feng, Zhiwei Yun, Wei Zhang
In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-sing…
Higher Siegel--Weil formula for unitary groups: the non-singular terms
Tony Feng, Zhiwei Yun, Wei Zhang
We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalize…
Shtukas and the Taylor expansion of -functions (II)
Zhiwei Yun, Wei Zhang
For arithmetic applications, we extend and refine our results in \cite{YZ} to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension of…
Shtukas and the Taylor expansion of -functions
Zhiwei Yun, Wei Zhang
We define the Heegner--Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with -modifications for an even integer . We prove an identity between (1) The -t…
Rigidity in automorphic representations and local systems
Zhiwei Yun
We introduce the notion of rigidity for automorphic representations of groups over global function fields. We construct the Langlands parameters of rigid automorphic representation…
Galois representations attached to moments of Kloosterman sums and conjectures of Evans
Zhiwei Yun
Kloosterman sums for a finite field arise as Frobenius trace functions of certain local systems defined over $\Gm$. The moments of Kloosterman sums calculate the Frobenius traces o…
Orbital integrals and Dedekind zeta functions
Zhiwei Yun
Let F be a local non-archimedean field. We prove a formula relating orbital integrals in GL(n,F) (for the unit Hecke function) and the generating series counting ideals of a certai…
Motives with exceptional Galois groups and the inverse Galois problem
Zhiwei Yun
We construct motivic -adic representations of $\GQ$ into exceptional groups of type and whose image is Zariski dense. This answers a question of Serre. The co…