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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:03:50 +0000Apparition and Periodicity Properties of Equianharmonic Divisibility Sequences
https://resolver.caltech.edu/CaltechTHESIS:10122017-094936829
Authors: {'items': [{'id': 'Durst-Lincoln-Kearney', 'name': {'family': 'Durst', 'given': 'Lincoln Kearney'}, 'show_email': 'NO'}]}
Year: 1952
DOI: 10.7907/4093-GY48
<p>Elliptic divisibility sequences were first studied by
Morgan Ward, who proved that they admit every prime p as a
divisor and gave the upper bound 2p + 1 for the smallest place
of apparition of p. He also proved that, except for a few
special primes, the sequences are numerically periodic modulo p.</p>
<p>This thesis contains a discussion of equanharmonic divisibility
sequences and mappings. These sequences are the special
elliptic sequences which occur when the elliptic functions involved
degenerate into equianharmonic functions, and the divisibility
mappings are an extensioin of the notion of a sequence to a function
over a certain ring of quadratic integers</p>
<p>For equianharmonic divisibility sequences and mappings an
arithmetical relation between any rational prime of the form 3k + 2
and its rank of apparition is found.</p>
<p>It is also shown that, except for a few special prime ideals,
equianharmonic divisibility mappings are numerically doubly periodic
to prime ideal moduli.</p>https://thesis.library.caltech.edu/id/eprint/10508