Bulletin of the American Mathematical Society Volume 19. American Mathematical Society
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Author: American Mathematical Society
Number of Pages: 192 pages
Published Date: 01 Mar 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
ISBN: 9781130447682
File Name: Bulletin.of.the.American.Mathematical.Society.Volume.19.pdf
Download Link: Bulletin of the American Mathematical Society Volume 19
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ... Galajikian and Dr. Sheffer were communicated to the Society through Dr. Hurwitz, that of Professor Caparo through Professor G. A. Miller. Dr. Hennel was introduced by Professor Carmichael, Mr. Love by Professor Ford. The papers of the following authors were read by title: Professor Carmichael, Professor Miller, Dr. Rowe, Professor Sharpe and Dr. Morgan, Dr. Sheffer, Dr. Conner, Professor Buchanan, Professor Evans, Professor Caparo, Professor Westlund, Dr. Dodd, Professor Kasner, Professor Keyser, Professor Ranum, Professor Eisenhart, Professor Huntington, Professor Frizell, Dr. Gronwall, Professor MacMillan, Professor Fite, Mr. Smail, Professor Snyder, Dr. Silverman. The second papers of Professor Dickson and Professor Karpinski were also read by title. Mr. Galajikian's paper was read by Dr. Hurwitz. Abstracts of the papers follow below. The abstracts are numbered to correspond to the titles in the list above. 1. Let a and /3 be the roots of the quadratic equation z2-(a + /3)z + a/3 = 0, whose coefficients a + /3 and a/3 are relatively prime integers such that a and /3 are not roots of unity. Then the numbers Dn and Sn, Dn =, S = a" + (8," a--p are integers. THe principal object of Professor Carmichael's first paper is an investigation of the numerical properties of Dn and S . The general results obtained have several applications in the theory of numbers. Among the factors of Dn and Sn are numbers of the form Fk(a, where Fka, /3) is that irreducible algebraic factor of ak--jS which is not a factor of any a"--for which v is less than k. These numbers Fk(x, /3) play a fundamental role throughout the paper. The general results cannot be briefly stated. Of the conclusions obtained in application of the general theorems we mention t...
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