Some topics on the Fourier coefficients of modular forms

Kaushik, S and Kumar, Narasimha (2018) Some topics on the Fourier coefficients of modular forms. PhD thesis, Indian institute of technology Hyderabad.

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This thesis consists of three parts. In the first part, we study the gaps between non-zero 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 half-integral 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 n-th Fourier coefficient of fE is non-zero 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(

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IITH Creators:
IITH CreatorsORCiD
Kumar, NarasimhaUNSPECIFIED
Item Type: Thesis (PhD)
Uncontrolled Keywords: Elliptic curves, CM eigenforms, Fourier coefficients, Hilbert modular forms of integral and half-integral weights, Sign changes, non-vanishing
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 30 Jul 2018 06:37
Last Modified: 30 Jul 2018 06:51
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