On the Fourier coefficients of Hilbert modular forms of half-integral weight over arbitrary algebraic number fields

Abstract

In Theorem 2.5 in previous paper [4], we determined the Fourier coefficients of the image of Shimura correspondence of modular forms f of half integral weight over arbitrary algebraic number fields in terms of those of f. It seems that there is a gap in the proof. We give a correct proof of Theorem 2.5 in [4]. Moreover, we deduce useful formulas between the product of Fourier coefficients of f and the central value of quadratic twisted L-series associated with the image of Shimura correspondence of f .