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On the number of integral ideals of given norm and ray-class
Published online by Cambridge University Press: 26 February 2010
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Let K be an algebraic number field, [K: Q] = κ є N; only the case κ > 1 is of interest in this paper. Let f be any non-zero ideal in ZK, the ring of integers of K, and let b be any ray-class (modx f) of K. In this paper we answer a question of P. Erdös (private communication) about the “maximum-growth-rate” of the functions
and
the sum here taken over all ray-classes (modx f), while N(a) is the absolute norm of a. Let
and
where, as usual, for x є R, log+ x - log max {1, x}. We prove
THEOREM 1. For every f, b we have
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- Copyright © University College London 1991
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