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- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Mathematisches Seminar der Universität Hamburg and Springer
- Subject
- Mathematics; Geometry; Combinatorics; Algebra; Topology; Number Theory; Differential Geometry
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/s12188-011-0059-y
- Publisher site
- See Article on Publisher Site
Abstract
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X 2+nY 2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Sep 2, 2011