math.NT — Number Theory

A trace upper-bound certificate with complex-root auxiliaries

Contributed by Ricardo Pinho

A rational piecewise-linear measure with 23 auxiliary polynomials gives $C_{86}\le1.80697883$ for the Schur--Siegel--Smyth trace constant. The proof uses Smith's arithmetic-measure criterion and converse theorem. Two degree-eight auxiliaries have nonreal roots; both polynomials already occur in Flammang (2009) and McKee (2011). Their use in this upper-bound certificate, rather than their discovery, is the change described here. This note is unrefereed, with no independent human review or formalization.