Kaushik, S and Kumar, Narasimha
(2018)
Some topics on the Fourier coefficients of
modular forms.
PhD thesis, Indian institute of technology Hyderabad.
Abstract
This thesis consists of three parts. In the first part, we study the gaps between
nonzero Fourier coefficients of cuspdial CM eigenforms in the short intervals. In
the second part, we study the sign changes for the Fourier coefficients of Hilbert
modular forms of halfintegral weight. In the third part, we study the simultaneous
behaviour of Fourier coefficients of two different Hilbert modular cusp forms
of integral weight.
In Chapter 1, we present the definitions and some preliminaries on classical
modular forms. We shall also recall some relevant results from the literature, which
are useful in the subsequent chapters.
In Chapter 2, we show that for an elliptic curve E over Q of conductor N with
complex multiplication (CM) by Q(i), the nth Fourier coefficient of fE is nonzero
in the short interval (X;X + cX
1
4 ) for all X � 0 and for some c > 0, where fE is
the corresponding cuspidal Hecke eigenform in S2(
[error in script]
IITH Creators: 
IITH Creators  ORCiD 

Kumar, Narasimha  UNSPECIFIED 

Item Type: 
Thesis
(PhD)

Uncontrolled Keywords: 
Elliptic curves, CM eigenforms, Fourier coefficients, Hilbert modular
forms of integral and halfintegral weights, Sign changes, nonvanishing 
Subjects: 
Mathematics 
Divisions: 
Department of Mathematics 
Depositing User: 
Team Library

Date Deposited: 
30 Jul 2018 06:37 
Last Modified: 
30 Jul 2018 06:51 
URI: 
http://raiith.iith.ac.in/id/eprint/4329 
Publisher URL: 

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