Mellin duality for the band-parity companion, formalized in Lean

Let p be an odd prime and χ an odd Dirichlet character modulo p. The multiplier family C_χ(a) = Σ_{0<n<p/2} χ(n)(−1)^{n+⟨an²⟩}, where ⟨x⟩ is the least nonnegative residue, has at a = 1 and for the quartic character the band-parity companion Σ_{0<n

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-30
DOI
https://doi.org/10.5281/zenodo.23796262
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Mellin duality for the band-parity companion, formalized in Lean

Joseph S. Farland
4 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Mellin duality for the band-parity companion, formalized in Lean

Joseph S. Farland
preprint en

Abstract

Let p be an odd prime and χ an odd Dirichlet character modulo p. The multiplier family C_χ(a) = Σ_{0<n<p/2} χ(n)(−1)^{n+⟨an²⟩}, where ⟨x⟩ is the least nonnegative residue, has at a = 1 and for the quartic character the band-parity companion Σ_{0<n

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Mellin duality for the band-parity companion, formalized in Lean — Joseph S. Farland · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS