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.
Sponsorship
Science Foundation Ireland
Other Sponsorship
Danish Agency for Science, Technology and Innovation
Type of Material
Journal Article
Publisher
Springer
Journal
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume
81
Start Page
129
End Page
139
Copyright (Published Version)
2011 Mathematisches Seminar der Universität Hamburg and Springer