Year: 2015
Type: article
Abstract: In 1975, Cohen constructed a kind of one-variable modular forms of half-integral weight, say [Formula: see text], whose [Formula: see text]th Fourier coefficient only occurs when [Formula: see text] is congruent to 0 or 1 modulo 4. The space of modular forms whose Fourier coefficients have the above property is called Kohnen plus space, initially introduced by Kohnen in 1980. Recently, Hiraga and Ikeda generalized the plus space to the spaces for half-integral weight Hilbert modular forms with respect to general totally real number fields. The [Formula: see text]th Fourier coefficients [Formula: see text] of a Hilbert modular form of parallel weight [Formula: see text] lying in the generalized Kohnen plus space does not vanish only if [Formula: see text] is congruent to a square modulo 4. In this paper, we use an adelic way to construct Eisenstein series of parallel half-integral weight belonging to the generalized Kohnen plus spaces and give an explicit form for their Fourier coefficients. These series give a generalization of the one introduced by Cohen. Moreover, we show that the Kohnen plus space is generated by the cusp forms and the Eisenstein series we constructed as a vector space over [Formula: see text].
Author: Ren-He Su
Institution: Kyoto University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 多変数の半整数ウェイトの保型形式とその応用
OpenAlex ID: W1865616495