19 citations · 115 across the 16 of their papers we have counts for
16 papers
Algebraicity of Spin -functions for
Ellen Eischen, Giovanni Rosso, Shrenik Shah
We prove algebraicity of critical values of certain Spin -functions. More precisely, our results concern for cuspidal automorphic representations as…
An introduction to Eisenstein measures
E. E. Eischen
This paper provides an introduction to Eisenstein measures, a powerful tool for constructing certain -adic -functions. First seen in Serre's realization of -adic Dedekind…
A Gallery of Gaussian Periods
Ellen Eischen, Stephan Ramon Garcia
Gaussian periods are certain sums of roots of unity whose study dates back to Gauss's seminal work in algebra and number theory. Recently, large scale plots of Gaussian periods hav…
Archimedean Zeta Integrals for Unitary Groups
Ellen Eischen, Zheng Liu
We derive precise formulas for the archimedean Euler factors occurring in certain standard Langlands -functions for unitary groups. In the 1980s, Paul Garrett, as well as Ilya P…
Entire theta operators at unramified primes
E. Eischen, E. Mantovan
Starting with work of Serre, Katz, and Swinnerton-Dyer, theta operators have played a key role in the study of -adic and modular forms and Galois representations. This…
Differential operators mod : analytic continuation and consequences
Ellen E. Eischen, Max Flander, Alexandru Ghitza +2
This paper concerns certain differential operators that act on automorphic forms over Shimura varieties of type A or C. We show that, over the ordinary locus, these operat…
-adic families of automorphic forms in the -ordinary setting
E. Eischen, E. Mantovan
We develop a theory of -adic automorphic forms on unitary groups that allows -adic interpolation in families and holds for all primes that do not ramify in the reflex fie…
Applications of nonarchimedean developments to archimedean nonvanishing results for twisted -functions
E. E. Eischen
We prove the nonvanishing of the twisted central critical values of a class of automorphic -functions for twists by all but finitely many unitary characters in particular infini…
p-adic L-functions for unitary groups
Ellen Eischen, Michael Harris, Jianshu Li +1
This paper completes the construction of -adic -functions for unitary groups. More precisely, in 2006, the last three named authors proposed an approach to constructing such…
Differential operators and families of automorphic forms on unitary groups of arbitrary signature
Ellen Eischen, Jessica Fintzen, Elena Mantovan +1
In the 1970's, Serre exploited congruences between -expansion coefficients of Eisenstein series to produce -adic families of Eisenstein series and, in turn, -adic zeta fun…
p-adic q-expansion principles on unitary Shimura varieties
Ana Caraiani, Ellen Eischen, Jessica Fintzen +2
We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms o…
Differential operators, pullbacks, and families of automorphic forms
Ellen Eischen
This paper has two main parts. First, we construct certain differential operators, which generalize operators studied by G. Shimura. Then, as an application of some of these differ…
p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups
Ellen Eischen, Xin Wan
We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signat…
A p-adic Eisenstein measure for vector-weight automorphic forms
Ellen Eischen
We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpol…
A p-adic Eisenstein measure for unitary groups
Ellen E. Eischen
We construct a p-adic Eisenstein measure with values in the space of p-adic automorphic forms on certain unitary groups. Using this measure, we p-adically interpolate certain speci…
p-adic Differential Operators on Automorphic Forms on Unitary Groups
Ellen E. Eischen
The goal of this paper is to study certain p-adic differential operators on automorphic forms on U(n,n). These operators are a generalization to the higher-dimensional, vector-valu…