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

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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Veröffentlicht in:The Ramanujan journal 2023-08, Vol.61 (4), p.1037-1062
Hauptverfasser: Nandi, Rimpa, Singh, Sujeet Kumar, Tiwari, Prashant
Format: Artikel
Sprache:eng
Schlagworte:
Coefficients
Combinatorics
Cusps
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Upper bounds
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Beschreibung
Zusammenfassung: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