Principal forms X-2 + nY^2 representing many integers

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Title: Principal forms X-2 + nY^2 representing many integers
Authors: Brink, David
Moree, Pieter
Osburn, Robert
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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 Universit├Ąt 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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