Tsukuba Journal of Mathematics

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

Hisashi Kojima

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 .

Article information

Source
Tsukuba J. Math., Volume 37, Number 1 (2013), 1-11.

Dates
First available in Project Euclid: 15 July 2013

https://projecteuclid.org/euclid.tkbjm/1373893402

Digital Object Identifier
doi:10.21099/tkbjm/1373893402

Mathematical Reviews number (MathSciNet)
MR3112415

Zentralblatt MATH identifier
1325.11040

Citation

Kojima, Hisashi. On the Fourier coefficients of Hilbert modular forms of half-integral weight over arbitrary algebraic number fields. Tsukuba J. Math. 37 (2013), no. 1, 1--11. doi:10.21099/tkbjm/1373893402. https://projecteuclid.org/euclid.tkbjm/1373893402