Generalized Kummer congruences and Iwasawa invariants

We obtain the following generalization of the Kummer congruence: $G\sb{c}(j,\chi,n) = -\left\lbrack{p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack {1\over n}(1 - \chiω\sp{-n}(p) p\sp{n-1}) B\sb{n,\chiω\sp{-n}}\in\doubz\sb{p}\lbrack\chi\rbrack ,$where $B\sb{n,\chi}$ is the generalized Bernoulli number associated to the Dirichlet character $\chi,\ \Delta\sb{\rm c}$ is the difference operator$\Delta\sb{\rm c} x\sb{n} = x\sb{n+c} - x\sb{n} {\rm and} \left\lbrack {p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack$is a binomial coefficient operator.

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

2011

Author dc:creator

• Gunaratne, Haputantirige Sunil

Contributors dc:contributor

• Ullom, Stephen V.

• Mathematics

Statement dc:rights

• Copyright 1991 Gunaratne, Haputantirige Sunil

Language dc:language

eng

Identifier

(UMI)AAI9210821
AAI9210821

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20942