Kummer type congruences and Stickelberger subideals
Kummer type system of congruences and bases of Stickelberger subideals
Kummer's Congruences (mod 2r).
Leudesdorf's theorem and Bernoulli numbers
For , , it is proved the relations between the sums and Bernoulli numbers. The result supplements the known theorems of C. Leudesdorf, N. Rama Rao and others. As the application it is obtained some connections between the sums and Agoh’s functions, Wilson quotients, the indices irregularity of Bernoulli numbers.
ℚ-linear relations of special values of the Estermann zeta function
Lower bounds for sums of powers of different natural numbers expressed as functions of the sum of these numbers.
Matrices of the Stickelberger ideals mod for all primes up to 125,000
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Mod p³ analogues of theorems of Gauss and Jacobi on binomial coefficients
Multiple p-adic log-gamma functions and their characterization theorem
Multiple twisted -Euler numbers and polynomials associated with -adic -integrals.
Multivariate interpolation functions of higher-order -Euler numbers and their applications.
Multivariate -adic fermionic -integral on and related multiple zeta-type functions.
Multivariate twisted -adic -integral on associated with twisted -Bernoulli polynomials and numbers.
Nonvanishing of a certain Bernoulli number and a related topic
Let be an odd prime number with q an odd integer. Let δ (resp. φ) be an odd (resp. even) Dirichlet character of conductor p and order (resp. order dividing q), and let ψₙ be an even character of conductor and order pⁿ. We put χ = δφψₙ, whose value is contained in . It is well known that the Bernoulli number is not zero, which is shown in an analytic way. In the extreme cases and q, we show, in an algebraic and elementary manner, a stronger nonvanishing result: for any pⁿth root ξ...
Note on -extensions of Euler numbers and polynomials of higher order.
Note on the -extension of Barnes' type multiple Euler polynomials.
Note sur le procédé le plus simple de calcul des nombres de Bernoulli
Note sur les sommes des puissances semblables des n premiers nombres entiers