Etale Homotopy and Sums-of-squares Formulas

An Application of Hermitian K-Theory: Sums-of-Squares Formulas

By using Hermitian K-theory, we improve D. Dugger and D. Isaksen’s condition (some powers of 2 dividing some binomial coefficients) for the existence of sums-of-squares formulas. 2010 Mathematics Subject Classification: 19G38; 11E25; 15A63

Sums-of-Squares Formulas

The following is the extended version of my notes from my ATC talk given on June 4, 2014 at UCLA. I begin with a basic introduction to sums-of-squares formulas, and move on to giving motivation for studying these formulas and discussing some results about them over the reals. More recent techniques have made it possible to obtain similar results over arbitrary fields, and some of these are disc...

Etale Cohomology of Rigid Analytic Spaces

The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...

Exact and Asymptotic Evaluation of the Number of Distinct Primitive Cuboids

We express the number of distinct primitive cuboids with given odd diagonal in terms of the twisted Euler function with alternating Dirichlet character of period four, and two counting formulas for binary sums of squares. Based on the asymptotic behaviour of the sums of these formulas, we derive an approximation formula for the cumulative number of primitive cuboids.

A Short Proof of Milne’s Formulas for Sums of Integer Squares