与虚二次域相关的权为1的艾森斯坦级数

Weight one Eisenstein series associated with

imaginary quadratic fields

SHEN Li-chien

【摘 要】Abstract:We consider a family of weight one Eisenstein series associated with the imaginary quadratic fields.The subspace of the Eisenstein series associated with the Kronecker symbol is characterized by the quadratic forms generated from the genus theory of Gauss;we will derive a family of identities connected with these quadratic fields. 【期刊名称】华东师范大学学报（自然科学版） 【年(卷),期】2019(000)002 【总页数】14 【

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Keywords:Eisenstein

series;Kronecker

symbol;discriminant;quadratic field;modular form CLC number:O174 Document code:A

Article ID:1000-5641(2019)02-0007-14

0 Introduction

This work focuses on the weight one Eisenstein series derived from the genus theory of imaginary quadratic fields.The relevant background material for this paper is provided in Section 1.Sections 2 and 3 contain a brief review of the genus characters of Gauss,correspondence between the ideals and the quadratic forms of the quadratic fields,and