Takashi Agoh

Shortened recurrence relations for Bernoulli numbers

Starting with two little-known results of Saalschutz, we derive a number of general recurrence relations for Bernoulli numbers. These relations involve an arbitrarily small number of terms and have Stirling numbers of both kinds as coefficients. As special cases we obtain explicit formulas for Bernoulli numbers, as well as several known identities.

On Bernoulli and Euler numbers

The main purpose of this paper is to investigate some basic relations (e.g., Voronois and Kummers congruences) of Bernoulli and Euler numbers by manipulating Euler factors in a natural way.

Reciprocity Relations for Bernoulli Numbers

(2008). Reciprocity Relations for Bernoulli Numbers. The American Mathematical Monthly: Vol. 115, No. 3, pp. 237-244.

On Giuga’s conjecture

In this paper we shall investigate Giuga’s conjecture which asserts an interesting characterization of prime numbers, just as Wilson’s Theorem. Some variations and consequences of the Giuga congruence are discussed by means of Bernoulli numbers. In addition, we shall study various quotients relating to the integers satisfying the Giuga congruence.

Wilson quotients for composite moduli

An analogue for composite moduli of the Wilson quotient is investigated. The Wilson numbers are studied and eight new Wilson numbers are found.

A note on unit and class number of real quadratic fields

Letp be an odd prime withp≡1 (mod 4) andQ(√p) be the real quadratic field. Also letε andh denote the fundamental unit and the class number of Q(√p), respectively. The main purpose of this paper is to study the “explicit” expressions ofεh andε2h, and to discuss the problems related to the conjecture of Ankeny-Artin-Chowla.

Convolution identities for Stirling numbers of the first kind

Abstract We derive several new convolution identities for the Stirling numbers of the first kind. As a consequence we obtain a new linear recurrence relation which generalizes known relations.

Quadratic equations over finite fields and class numbers of real quadratic fields

AbstractLetp be an odd prime and

Primes at a (Somewhat Lengthy) Glance

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