Journal of Algebra, Number Theory: Advances and Applications
ARITHMETIC FUNCTION AND PRIMITIVE FOUR
SQUARES Author's: Werner Hürlimann
Pages: [73] - [88]
Received Date: December 8, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121599
We define summatory odd and even Dedekind arithmetic functions and obtain their first order asymptotic estimates. Based on this, we determine an asymptotic formula for the cumulative number of primitive four squares representations, which compares with Landau’s original formula for arbitrary four squares representations. The introduced arithmetic functions are also used to study the asymptotic behaviour of the cumulative number of distinct primitive Pythagorean quintuples. A conjecture is formulated at the end of the paper.
sum of squares, primitive representation, Pythagorean quintuple, Dedekind arithmetic function.
