On a theta correspondence with respect to a quadratic extension
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 \(I(z,h)\).
scientific article; zbMATH DE number 1389287