Dirichlet series associated to Modular forms
Material type:
TextPublication details: 1990Description: ix; 42pSubject(s): Mathematics | Dirichlet Series | Modular FormsOnline resources: Click here to access online Dissertation note: 1990Ph.DUniversity of Madras Abstract: Waring's problem, Goldbach's conjecture, Dirichlet divisor problem and the order of Dirichlet series in critical strip are good examples for the phenomena in Number theory, 'for a problem reducing in the ultimate analysis to estimating an exponential sum'. This thesis is concerned with functional equations for Dirichlet series and their twists by additive characters associated to arithmetic modular forms, for congruence subgroups of the full modular group SL(2, Z). Transformation formulae for exponential sums involving Fourier Coefficients of cusp forms are obtained; To show that "all those applications of transformation formula, obtained by M. Jutila, for 'Dirichlet series associated to cusp forms, for the full modular group' are valid in the case of Dirichlet series coming from arithmetic cusp forms for congruence subgroups of SL(2, Z)", two sample applications of the transformation formula are given as examples. Some theorems, Lemmas and corollary are explained and proved.
THESIS & DISSERTATION
| Current library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| IMSc Library | IMSc Library | UNM Th-37 (Browse shelf (Opens below)) | Link to resource | Available | 26911 |
1990
Ph.D
University of Madras
Waring's problem, Goldbach's conjecture, Dirichlet divisor problem and the order of Dirichlet series in critical strip are good examples for the phenomena in Number theory, 'for a problem reducing in the ultimate analysis to estimating an exponential sum'. This thesis is concerned with functional equations for Dirichlet series and their twists by additive characters associated to arithmetic modular forms, for congruence subgroups of the full modular group SL(2, Z). Transformation formulae for exponential sums involving Fourier Coefficients of cusp forms are obtained; To show that "all those applications of transformation formula, obtained by M. Jutila, for 'Dirichlet series associated to cusp forms, for the full modular group' are valid in the case of Dirichlet series coming from arithmetic cusp forms for congruence subgroups of SL(2, Z)", two sample applications of the transformation formula are given as examples. Some theorems, Lemmas and corollary are explained and proved.
There are no comments on this title.