کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4594918 | 1335788 | 2008 | 18 صفحه PDF | دانلود رایگان |

Let p be a prime, and let Zp denote the field of integers modulo p. The Nathanson height of a point is the sum of the least nonnegative integer representatives of its coordinates. The Nathanson height of a subspace is the least Nathanson height of any of its nonzero points. In this paper, we resolve a quantitative conjecture of Nathanson [M.B. Nathanson, Heights on the finite projective line, Int. J. Number Theory, in press], showing that on subspaces of of codimension one, the Nathanson height function can only take values about . We show this by proving a similar result for the coheight on subsets of Zp, where the coheight of A⊆Zp is the minimum number of times A must be added to itself so that the sum contains 0. We conjecture that the Nathanson height function has a similar constraint on its range regardless of the codimension, and produce some evidence that supports this conjecture.
Journal: Journal of Number Theory - Volume 128, Issue 9, September 2008, Pages 2616-2633