Norms of sums of squares

on direct sums of baer modules

the notion of baer modules was defined recently

Sums of distinct squares

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...

Sums of Two Squares

n = 1: 1 = 0 + 1; n = 2 (prime): 2 = 1 + 1; n = 3 (prime) is not a sum of two squares. n = 4: 4 = 2 + 0. n = 5 (prime): 5 = 2 + 1. n = 6 is not a sum of two squares. n = 7 (prime) is not a sum of two squares. n = 8: 8 = 2 + 2. n = 9: 9 = 3 + 0. n = 10: 10 = 3 + 1. n = 11 (prime) is not a sum of two squares. n = 12 is not a sum of two squares. n = 13 (prime): 13 = 3 + 2. n = 14 is not a sum of t...

Sums of Squares of |ζ(

Sums of squares of |ζ(1 2 + it)| over short intervals are investigated. Known upper bounds for the fourth and twelfth moment of |ζ(1 2 + it)| are derived. A discussion concerning other possibilities for the estimation of higher power moments of |ζ(1 2 + it)| is given.