Principal forms X-2 + nY^2 representing many integers
|Title:||Principal forms X-2 + nY^2 representing many integers||Authors:||Brink, David
|Permanent link:||http://hdl.handle.net/10197/7828||Date:||Oct-2011||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.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Springer||Copyright (published version):||2011 Mathematisches Seminar der Universität Hamburg and Springer||Keywords:||Binary quadratic forms;Bernays' constant;Special values of L-series;Quadratic-forms||DOI:||10.1007/s12188-011-0059-y||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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