On sign changes of Fourier coefficients of Hermitian cusp forms of degree two

We prove a quantitative result for the number of sign changes of the Fourier coefficients of a Hermitian cusp form of degree 2. In addition, we prove a quantitative result for the number of sign changes of the primitive Fourier coefficients. We give an explicit upper bound for the first sign change...

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Bibliographic Details
Published inThe Ramanujan journal Vol. 61; no. 4; pp. 1037 - 1062
Main Authors Nandi, Rimpa, Singh, Sujeet Kumar, Tiwari, Prashant
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2023
Springer Nature B.V
Subjects
Coefficients
Combinatorics
Cusps
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Upper bounds
Hermitian Jacobi forms
Jacobi forms with matrix index
Hermitian modular forms
Sturm bound
11F50
Sign changes
11F33
11F55
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Summary:We prove a quantitative result for the number of sign changes of the Fourier coefficients of a Hermitian cusp form of degree 2. In addition, we prove a quantitative result for the number of sign changes of the primitive Fourier coefficients. We give an explicit upper bound for the first sign change of the Fourier coefficients of a Hermitian cusp form of degree 2 over certain imaginary quadratic extensions.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-023-00716-2