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Stark units for real quadratic fields and reciprocity laws

A mix of human-written and AI-generated textHuman understanding: all partsmath.NT — Number Theorymath.QA — Quantum Algebra

Contributed by Danylo Radchenko ↗, Campbell Wheeler

Version 1 / Oct 10, 2026 / CC BY 4.0

Abstract

We prove that every value of the arithmetic finite quantum dilogarithms constructed by Radchenko and Wheeler (arXiv:2609.21892) is an algebraic unit, and determine the Artin action for arbitrary quadratic pseudolattices. In particular, the associated Stark units belong to the predicted ray class fields and have the predicted Galois action. We use finite Fourier transforms and distribution relations to obtain Frobenius congruences. We also give conductor bounds for individual values and obtain the unitary conjugates needed for Zauner's conjecture.

Provenance statement

Large language models were used to develop the arguments and draft much of the text. The human contributors checked the arguments and edited the exposition. A detailed account of the work's provenance is given in the paper's Disclaimer.

References

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Version history

  1. v1Submitted by Danylo RadchenkoInitial depositCurrentOct 10, 2026