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Remark on the number of classes of binary quadratic forms of a given negative determinant

Bell, E. T. (1928) Remark on the number of classes of binary quadratic forms of a given negative determinant. Proceedings of the National Academy of Sciences of the United States of America, 14 (5). pp. 430-431. ISSN 0027-8424. https://resolver.caltech.edu/CaltechAUTHORS:BELpnas28a

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Abstract

On p. 254 of Mathews' "Theory of Numbers," Part I, 1892 (all that was published), we find the following clear statement of a desideratum that has often been expressed. "... leads to the conclusion that in the series 1, 2, 3, ... (p-1)/2 (p is an odd prime), there are more quadratic residues of p than non-residues. It does not appear that any independent proof of this proposition has ever been discovered. If any such proof could be found, it is not impossible that it might lead to a determination of h (the number of classes described in the title of this note) without the use of infinite series. Similar remarks apply to the other formulae for negative determinants."


Item Type:Article
Additional Information:Copyright © 1928 by the National Academy of Sciences. Communicated March 31, 1928.
Issue or Number:5
Record Number:CaltechAUTHORS:BELpnas28a
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:BELpnas28a
Alternative URL:http://www.pnas.org/content/vol14/issue5/
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4607
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Aug 2006
Last Modified:02 Oct 2019 23:14

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