3 papers
math.NT2022
An Inner Product on Adelic Measures: With Applications to the Arakelov-Zhang Pairing
Peter J. Oberly
We define an inner product on a vector space of adelic measures over a number field. We find that the norm induced by this inner product governs weak convergence at each place of $…
math.DS2021
A Remarkable Summation Formula, Lattice Tilings, and Fluctuations
J. J. P. Veerman, L. S. Fox, P. J. Oberly
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any re…
math.MG2020
One-Sided Derivative of Distance to a Compact Set
Logan S. Fox, Peter Oberly, J. J. P. Veerman
We give a complete and self-contained proof of a folklore theorem which says that in an Alexandrov space the distance between a point on a geodesic and a compact set …