In Theorem 2.5 in previous paper , 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 . 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 .
"On the Fourier coefficients of Hilbert modular forms of half-integral weight over arbitrary algebraic number fields." Tsukuba J. Math. 37 (1) 1 - 11, July 2013. https://doi.org/10.21099/tkbjm/1373893402