Geodesic
On the Distribution of M-tuples of B-numbers
Publications de l'Institut Mathématique, _N_S_77 (2005) no. 91, p. 71 .

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In the classical sense, the set $B$ consists of all integers which can be written as a sum of two perfect squares. In other words, these are the values attained by norms of integral ideals over the Gaussian field $\Qi(i)$. G. J. Rieger (1965) and T. Cochrane. R. E. Dressler (1987) established bounds for the number of pairs $(n,n+h)$, resp., triples $(n,n+1,n+2)$ of $B$-numbers up to a large real parameter $x$. The present article generalizes these investigations into two directions: The result obtained deals with arbitrary $M$-tuples of arithmetic progressions of positive integers, excluding the trivial case that one of them is a constant multiple of one of the others. Furthermore, the estimate applies to the case of an arbitrary normal extension $K$ of the rational field instead of $\Qi(i)$.
DOI : 10.2298/PIM0591071N
Classification : 11P05 11N35
Keywords: $B$-numbers, Selberg sieve, norms of ideals in number fields 
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     title = {On the {Distribution} of {M-tuples} of {B-numbers}},
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Werner Georg Nowak. On the Distribution of M-tuples of B-numbers. Publications de l'Institut Mathématique, _N_S_77 (2005) no. 91, p. 71 . doi : 10.2298/PIM0591071N. http://geodesic.mathdoc.fr/articles/10.2298/PIM0591071N/

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