Oscillating spectra associated to certain sequences draft1jun26

Key Points

• The research aims to explore the relationship between certain arithmetic sequences and oscillating matrix spectra derived from Fourier expansions.
• Studied numerical sequences derived from Fourier expansions of cusp forms.
• Observed and collected data on oscillatory behavior of associated matrices.
• Initiated testing of vectors spaces formed by sequences exhibiting oscillatory behavior.
• Identified oscillatory behavior in specific sequences within the study's observational range.
• Proposed the existence of vector spaces formed by the sequences exhibiting oscillatory behavior.

Abstract