## Tsukuba Journal of Mathematics

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

### 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*
.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 15 July 2013

**Permanent link to this document**

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