arXiv subjects

Eugene Ha

Publications and source records attributed to Eugene Ha.

3 recordsLinked to original sources

arXiv2026

A variation of Eichler's proof of the Baker-Campbell-Hausdorff formula

Eichler gave an elementary but involved proof of the Baker-Campbell-Hausdorff formula, based on the associativity of the product of three exponentials. We show that by considering the associativity of the product of four exponentials, one can bypass the complications of Eichler's proof to arrive at a shorter proof that is both elementary and straightforward. As a corollary of the proof, a recursive scheme for the Baker-Campbell-Hausdorff formula is derived, in which explicit Bernoulli numbers are notably absent.

math.RA↗

arXiv2015

Fredholm modules and the Beilinson-Bloch regulator

We prove an operator-theoretic reconstruction of the Beilinson-Bloch regulator for compact Riemann surfaces, using loop operators and the Connes-Karoubi character for Fredholm modules. The proof includes a new computation of the Connes-Karoubi character for Steinberg symbols of the circle, which relies on the Helton-Howe determinant theory, but not on the Carey-Pincus theory of joint torsion.

math.OA↗

arXiv2005

Bost-Connes-Marcolli systems for Shimura varieties. I. Definitions and formal analytic properties

We construct a quantum statistical mechanical system $(A,s)$ analogous to the systems constructed by Bost-Connes and Connes-Marcolli in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which has the ``correct'' partition function and the ``correct'' symmetries. We give a formalism that applies to general Shimura data $(G,X)$. The object of this series of papers is to show that these systems exhibit phase transitions with spontaneous symmetry breaking, and to classify their KMS states, at least for low temperature.

math.OA↗