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2013•Unpublished venueRequires access

Dimensions of Modular Forms and Cusp Forms over Modular Group

Amit Kumar

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Abstract

The theory of modular forms was developed by Hecke and others while attempting to prove Ramanujan's conjectures, a collection of three conjectures on the τ-function. The space of modular forms over SL2(Z) and its congruence subgroups form a C vector space. This thesis is about the study of the dimension(s) of these vector spaces over SL2(Z) and its congruence subgroups.

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What this paper is about

The theory of modular forms was developed by Hecke and others while attempting to prove Ramanujan's conjectures, a collection of three conjectures on the τ-function. The space of modular forms over SL2(Z) and its congruence subgroups form a C vector space. This thesis is about the study of the dimension(s) of these vector spaces over SL2(Z) and its congruence subgroups.

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Available abstract

The theory of modular forms was developed by Hecke and others while attempting to prove Ramanujan's conjectures, a collection of three conjectures on the τ-function. The space of modular forms over SL2(Z) and its congruence subgroups form a C vector space. This thesis is about the study of the dimension(s) of these vector spaces over SL2(Z) and its congruence subgroups.

Key concepts: SL2(R), Modular form, Hecke operator, Modular group, Ramanujan's sum, Congruence subgroup, Mathematics, Cusp form

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