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On the Distribution of Squares of Hypercomplex Integers

โœ Scribed by G. Kuba

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
185 KB
Volume
88
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let A be a real quadratic algebra of dimension s 3 which satisfies the basic relations of hypercomplex systems. For a large positive parameter X, let A(X) denote the number of squares : 2 with : # A, : integral, and all s components of : 2 lying in the interval [&X, X]. With particular regard to Cayley's octaves, and generalizing former results concerning Gaussian integers by H. Mu ller and W. G. Nowak, and Hurwitz integral quaternions by the author, we show that

where c and d are certain positive constants depending on s, and $(X) is any upper bound of the error term in the divisor problem, e.g. $(X )=X 23ร‚73+= .

2001

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