Dirichlet series associated to Modular forms

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Dirichlet series associated to Modular forms

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dc.contributor.author Yogananda, C. S.
dc.date.accessioned 2009-08-10T07:45:56Z
dc.date.available 2009-08-10T07:45:56Z
dc.date.issued 2009-08-10T07:45:56Z
dc.date.submitted 1990
dc.identifier.uri http://hdl.handle.net/123456789/60
dc.description.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. en_US
dc.publisher.publisher
dc.subject Modular Forms en_US
dc.subject Dirichlet Series en_US
dc.title Dirichlet series associated to Modular forms en_US
dc.type.degree Ph.D en_US
dc.type.institution University of Madras en_US
dc.description.advisor Balasubramanian, R.
dc.description.pages ix; 42p. en_US
dc.type.mainsub Mathematics en_US

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