On a theta correspondence with respect to a quadratic extension
type: Item
instance of: scholarly article
title: On a theta correspondence with respect to a quadratic extension
zbMATH Open document ID: 0943.11025
author: Ze-Li Dou
published in: Journal of Number Theory
publication date: 2000-09-04T00:00:00Z
review text: Let \(E\) be a totally real quadratic extension of a totally real number field \(F\), and let \(B_E\) be a quaternion algebra over \(E\) equipped with an \(F\)-linear automorphism \(\tau\) with \(\tau^2 = 1_{B_E}\) and \(\tau |_E \neq 1_E\). Given a suitably defined automorphic form \(h\) with respect to the quaternion algebra \(B_E\), the author constructs a Hilbert modular form \(I(z,h)\) defined with respect to the field \(F\) by using a convolution of \(h\) with a theta function. He then obtains an explicit formula for the Fourier coefficients of \(I(z,h)\).
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 1389287
zbMATH Keywords: Hilbert modular forms
zbMATH Keywords: theta correspondence
zbMATH Keywords: quaternionic automorphic forms
MaRDI profile type: Publication
full work available at URL: jnth.1999.2416
OpenAlex ID: W2075445952
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DOI: 10.1006/JNTH.1999.2416
description: scientific article; zbMATH DE number 1389287