منابع مشابه
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...
متن کاملSums 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...
متن کاملSums 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.
متن کاملOn Sums of Three Squares
(1) r3(n) = 4πn S3(n), where the singular series S3(n) is given by (16) with Q = ∞. While in principle this exact formula can be used to answer almost any question concerning r3(n), the ensuing calculations can be tricky because of the slow convergence of the singular series S3(n). Thus, one often sidesteps (1) and attacks problems involving r3(n) directly. For example, concerning the mean valu...
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ژورنال
عنوان ژورنال: Journal of Software for Algebra and Geometry
سال: 2020
ISSN: 1948-7916
DOI: 10.2140/jsag.2020.10.17