University of Illinois at Urbana-Champaign
Zeros of P-Adic L-Functions and Densities Relating to Bernoulli Numbers
Abstract
dc:descriptionA prime p is said to be irregular if it divides the numerator of the Bernoulli number B(,i) for some even integer i between 1 and p-2. For every irregular pair (p,i) with p < 125,000 it is known that the corresponding p-adic L-function L(,p)(s,(chi)(,i)) of Kubota and Leopoldt has a unique zero ('i)(kappa) in the p-adic integers. For every irregular pair (p,i) with p < 1000, several p-adic places of ('i)(kappa) are calculated using a p-adic Newton's method and the formula for L(,p)(s,(chi)(,i)) derived by L. Washington. After the calculation the zeros ('i)(kappa) are transformed to zeros ('i-1)(omega) of corresponding p-adic power series used in the study of cyclotomic fields and defined by Iwasawa.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Sunseri, Richard Frank
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8017995
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/68168