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1、On Eisenstein series generated from twisting of the geometric seriesSHEN Li-chien【摘 要 Abstractsn this paper,we will be dealing with thetwistingofgeometricseries bythe Dirichletcharacters.Inconjunctionwiththebasic toolof Fouriertransform,itcan be usedto generate alltheEisenstein series with respect t
2、o a family arithmetic groups.【期刊名称】 华东师范大学学报（自然科学版） 【年（卷）,期】2017（000）006【总页数】 24【 关 键 词 】 Key words:Dirichlet character;conductor;Eisenstein series;Gaussian sum;Kronecker symbol;Mellin transform;modular form;Poisson summation formula;Weil s converse theorem The paper is organized as follows.The rele
3、vant properties of the Dirichlet characters and the geometric series twisted by the primitive characters are given in Sections 0 and 1.Sections 2 and 3 consist of the Mellin transform of the twisted geometric series,the derivation of the associated Fourier transform and a family of functions invariant under the Fourier transform.TheEise nste in series of weight k 3 gen eratedby the twisted Poiss onsummation formula are derived in Sections 4,5,6 and 7.In Sections 8 and9,we provide the statement of Weil s Converse Theorem as well as the
