The valuative capacity of the set of sums of d-th powers

JOURNAL OF NUMBER THEORY

卷:171

Article

关键词: Integer valued polynomials;    Valuative capacity;    p-Orderings;    Sums of powers;   

DOI  :  10.1016/j.jnt.2016.07.006

来源: Elsevier

【 摘 要 】

If E is a subset of the integers then the n-th characteristic ideal of E is the fractional ideal of Z consisting of 0 and the leading coefficients of the polynomials in Q[x] of degree no more than n which are integer valued on E. For p a prime the characteristic sequence of Int(E, Z) is the sequence alpha(E) (n) of negatives of the p-adic valuations of these ideals. The asymptotic limit lim(n ->infinity) alpha(E,p)(n)/n of this sequence, called the valuative capacity of E, gives information about the geometry of E. We compute these valuative capacities for the sets E of sums of l >= 2 integers to the power of d, by observing the p-adic closure of these sets. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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