Investigates oscillatory matrix spectra in arithmetic sequences, suggesting vector space structure.
Identities originatingin the theory of symmetric functions expressmembers of arithmetic sequences as determinants. In this setting we studied numerically sequences (n) ≥ 1derived from the Fourier expansions of cusp forms.We observed that, within the range of our observations, in certain cases the spectra of matrices we attached to these sequences exhibit oscillatory behavior. We collect data on this behavior in some other sequences. We propose that sequences exhibiting oscillatory behavior may form vector spaces. We initiate testing of this proposal.
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Barry Brent (2026) studied this question.
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