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February 28, 20260 citationsOpen Access

TEBAC HP–E2N: E2 Determinant Package on GL(1) and Canonical Normalization

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TKTosho Lazarov Karadzhov

Key Points

  • The aim is to develop a canonical heat trace and its corresponding zeta determinant for the GL(1) operator.
  • Constructed a canonical centered heat trace for the $GL(1)$ operator.
  • Applied Mellin/zeta regularization for the heat trace.
  • Developed a scheme-independence theorem for admissible cutoff schemes.
  • Formulated a quotient to eliminate constant ambiguity in normalization limits.
  • Derived a canonical zeta determinant from the constructed heat trace.
  • Established explicit entire correction factors for scheme-independence.
  • Demonstrated the effectiveness of the canonical normalization limits.

Abstract

We construct a canonical centered heat trace and its Mellin/zeta regularization for the GL (1) operator from HP--II. This yields a canonical zeta determinant \ _^can (L+) \ and a scheme-independence theorem reducing any admissible cutoff/subtraction scheme (, , P₅₈₍₀₋) to the canonical object via an explicit entire correction factor. We also prove the canonical normalization limits needed to remove the constant ambiguity in the quotient \ Q (s) \;=\;D₂₎₌₏ (ₒ) (s) \,. \

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Cite This Study

Tosho Lazarov Karadzhov (2026) studied this question.

synapsesocial.com/papers/69a286720a974eb0d3c015c9https://doi.org/10.5281/zenodo.18783994
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