文献类型：期刊文献

英文题名：SPECIAL VALUES OF SHIFTED DIRICHLET SERIES AND QUASI-MODULAR FORMS

作者：Wang, Wei[1]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing 312000, Peoples R China

年份：2024

卷号：152

期号：11

起止页码：4633

外文期刊名：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

收录：SCI-EXPANDED(收录号：WOS:001381973100008)、、Scopus(收录号：2-s2.0-85205723840)、WOS

基金：This work was supported by NSFC 11701272 and NSFC 12071221.

语种：英文

外文关键词：Key words and phrases. Shifted Dirichlet series; quasi-modular forms; almost holomorphic modular forms

外文摘要：Multiplication by a given modular form can be viewed as a linear map on the space of modular forms. By computing its adjoint operator, one can obtain certain cusp forms whose Fourier coefficients are special values of Dirichlet series of Rankin-Selberg type associated to modular forms. We generalize this idea to the space of almost holomorphic modular forms with some cuspidal conditions. We prove that the generating function of special values of the Dirichlet series at certain points is a quasi-modular form.