Add to ORKGWe explore the Bernoulli numbers: a sequence of rational numbers with connections to combinatorics, complex analysis, algebraic number theory, etc. Importantly, Bernoulli numbers may be used to define the B-regular and B-irregular primes, which have historical connections to investigations of Fermat’s Last Theorem. In 1850, Ernst Kummer related B-irregularity of primes to the class numbers of cyclotomic fields. Over the course of this project, we build towards an understanding of this connection and its mathematical significance
The first appearance of the set of rational numbers of which I am speaking was in James Bernoulli\u2...
Let p be an odd prime. It is called irregular if and only if p divides the class number of Q(µp). By...
AbstractIn this paper we use Redei′s work on the class groups of quadratic number fields to generali...
I will recall what are the objects of the title and explain how one can combine them in a new way to...
The aim of this work is to study the relation between regular primes and regular Bernoulli numbers (...
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
AbstractLet k be a rational function field over a finite field. Carlitz and Hayes have described a f...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Inspired by a result of Saalschutz, we prove a recurrence relation for Bernoulli numbers. This recur...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
AbstractIn this paper there is shown a “certain addition” to Iwasawa's class number formula for cycl...
Abstract: In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voron...
AbstractLet p be a finite prime of the rational function field K=Fq(T) and K(p): K the pth cyclotomi...
AbstractConditions for divisibility of class numbers of algebraic number fields by prime powers are ...
The first appearance of the set of rational numbers of which I am speaking was in James Bernoulli\u2...
Let p be an odd prime. It is called irregular if and only if p divides the class number of Q(µp). By...
AbstractIn this paper we use Redei′s work on the class groups of quadratic number fields to generali...
I will recall what are the objects of the title and explain how one can combine them in a new way to...
The aim of this work is to study the relation between regular primes and regular Bernoulli numbers (...
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
AbstractLet k be a rational function field over a finite field. Carlitz and Hayes have described a f...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Inspired by a result of Saalschutz, we prove a recurrence relation for Bernoulli numbers. This recur...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
AbstractIn this paper there is shown a “certain addition” to Iwasawa's class number formula for cycl...
Abstract: In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voron...
AbstractLet p be a finite prime of the rational function field K=Fq(T) and K(p): K the pth cyclotomi...
AbstractConditions for divisibility of class numbers of algebraic number fields by prime powers are ...
The first appearance of the set of rational numbers of which I am speaking was in James Bernoulli\u2...
Let p be an odd prime. It is called irregular if and only if p divides the class number of Q(µp). By...
AbstractIn this paper we use Redei′s work on the class groups of quadratic number fields to generali...