A remark on the number field analogue of Waring's constant g(k)

Paul Pollack

Mathematische Nachrichten, 2018, vol. 291, issue 11-12, 1893-1898

Abstract: Let K be a number field, and let k be an integer with k≥2. Let O≥0 be the collection of totally nonnegative integers in K (i.e., the totally positive integers together with zero). We let g(k,K) denote the smallest positive integer with the following property: Every element of O≥0 that is a sum of kth powers of elements of O≥0 is the sum of g such kth powers. Work of Siegel in the 1940s shows that g(k,K) is well‐defined for all k and K. In this note, we prove that g(k,K) cannot be bounded by a function of k alone: For each k≥2, supKg(k,K)=∞.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700320

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:291:y:2018:i:11-12:p:1893-1898

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().