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 X2+nY2. 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. © 2011 Mathematisches Seminar der Universität Hamburg and Springer.
CITATION STYLE
Brink, D., Moree, P., & Osburn, R. (2011). Principal forms X2+nY2 representing many integers. Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 81(2), 129–139. https://doi.org/10.1007/s12188-011-0059-y
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