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Apparition and Periodicity Properties of Equianharmonic Divisibility Sequences


Durst, Lincoln Kearney (1952) Apparition and Periodicity Properties of Equianharmonic Divisibility Sequences. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4093-GY48.


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.

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

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.

It is also shown that, except for a few special prime ideals, equianharmonic divisibility mappings are numerically doubly periodic to prime ideal moduli.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ward, Morgan
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:10122017-094936829
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10508
Deposited By: Benjamin Perez
Deposited On:12 Oct 2017 19:34
Last Modified:10 May 2023 23:46

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