On the distribution of algebraic primes in small regions (Q403143)

It has been shown by \textit{P. X. Gallagher} [Mathematika 23, 4--9 (1976; Zbl 0346.10024), corr. 28, 86 (1981; Zbl 0458.10029)] that if a uniform version of the \(k\)-tuple conjecture is true, then the distribution of prime numbers in short intervals is Poissonian. An analogue of that conjecture for algebraic number fields \(K\) has been formulated by \textit{R. Gross} and \textit{J. H. Smith} [Rocky Mt. J. Math. 30, No. 1, 195--215 (2000; Zbl 0978.11064)]. The authors show that the last conjecture implies a Poissonian distribution of integers of \(K\) in small regions, generating prime ideals.