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Arithmetical Properties of Polynomials Associated with the Lemniscate Elliptic Functions

Ward, Morgan (1950) Arithmetical Properties of Polynomials Associated with the Lemniscate Elliptic Functions. Proceedings of the National Academy of Sciences of the United States of America, 36 (6). pp. 359-362. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:MORpnas50

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Abstract

The arithmetical properties of the polynomials Pµ closely parallel the properties of Lucas' Un. The main new feature of interest (not occurring in the real multiplication case) is a genuine double numerical periodicity when the free variables z and w are given fixed values in G, and the residues of the resulting sequence in G are considered for moduli in G. Indeed Lucas claimed in his fundamental paper and elsewhere to have discovered doubly periodic numerical functions connected with the elliptic functions, but he apparently published nothing on this subject. [4]


Item Type:Article
Additional Information:Copyright © 1950 by the National Academy of Sciences Communicated by H. S. Vandiver, April 18, 1950 A more complete account of these and other results with proofs will be published elsewhere.
Record Number:CaltechAUTHORS:MORpnas50
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MORpnas50
Alternative URL:http://www.pnas.org/content/vol36/issue6/
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4526
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:27 Aug 2006
Last Modified:14 Nov 2014 19:19

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