math.NT — Number Theory
Stark units for real quadratic fields and reciprocity laws
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.
A mix of human-written and AI-generated textHuman understanding: all partsArtin reciprocityFrobenius congruencesReal quadratic fieldsStark unitsfinite quantum dilogarithmsray class fields