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is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose...

Local coefficients and normalization of intertwining operators for $G L (n)$

Freydoon Shahidi (1983)

Compositio Mathematica

Local Indecomposability of Hilbert Modular Galois Representations

Bin Zhao (2014)

Annales de l’institut Fourier

We prove the indecomposability of the Galois representation restricted to the $p$ -decomposition group attached to a non CM nearly $p$ -ordinary weight two Hilbert modular form over a totally real field $F$ under the assumption that either the degree of $F$ over $ℚ$ is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of $F$ .

Local Shimura Correspondence.

Gordan Savin (1988)

Mathematische Annalen

Local $ε_{0}$ -characters in torsion rings

Seidai Yasuda (2007)

Journal de Théorie des Nombres de Bordeaux

Let $p$ be a rational prime and $K$ a complete discrete valuation field with residue field $k$ of positive characteristic $p$ . When $k$ is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local $ε_{0}$ -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic $\neq p$ , of the Weil group $W_{K}$ of $K$ . In this paper, we generalize the results in [10] and [11] to the case where $k$ is an arbitrary perfect field.

Local-global compatibility for $l = p$ , I

Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the compatibility of the local and global Langlands correspondences at places dividing $l$ for the $l$ -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of ${GL}_{n}$ over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing $l$ and have Shin-regular weight.

Locally analytic vectors of unitary principal series of ${GL}_{2} (ℚ_{p})$

Ruochuan Liu, Bingyong Xie, Yuancao Zhang (2012)

Annales scientifiques de l'École Normale Supérieure

The $p$ -adic local Langlands correspondence for ${GL}_{2} (ℚ_{p})$ attaches to any $2$ -dimensional irreducible $p$ -adic representation $V$ of $G_{ℚ_{p}}$ an admissible unitary representation $Π (V)$ of ${GL}_{2} (ℚ_{p})$ . The unitary principal series of ${GL}_{2} (ℚ_{p})$ are those $Π (V)$ corresponding to trianguline representations. In this article, for $p > 2$ , using the machinery of Colmez, we determine the space of locally analytic vectors $Π {(V)}_{an}$ for all non-exceptional unitary principal series $Π (V)$ of ${GL}_{2} (ℚ_{p})$ by proving a conjecture of Emerton.

Logarithmic derivatives of Dirichlet $L$ -functions and the periods of abelian varieties

Greg W. Anderson (1982)

Compositio Mathematica

Logarithmic vector-valued modular forms

Marvin Knopp, Geoffrey Mason (2011)

Acta Arithmetica

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