O součtu čísel kubických
O součtu m-tých mocnin čísel řady přirozené
On a Bernoulli numbers conjectures.
On a congruence of Emma Lehmer related to Euler numbers
A congruence of Emma Lehmer (1938) for Euler numbers modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which play an important role, and we present some numerical results.
On a diophantine equation involving quadratic characters
On a two-variable -adic -function.
On asymptotic constants related to products of Bernoulli numbers and factorials.
On Bernoulli identities and applications.
Bernoulli numbers appear as special values of zeta functions at integers and identities relating the Bernoulli numbers follow as a consequence of properties of the corresponding zeta functions. The most famous example is that of the special values of the Riemann zeta function and the Bernoulli identities due to Euler. In this paper we introduce a general principle for producing Bernoulli identities and apply it to zeta functions considered by Shintani, Zagier and Eie. Our results include some of...
On Carlitz's type -Euler numbers associated with the fermionic -adic integral on .
On certain generalized q-Appell polynomial expansions
We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to...
On divisibility of the class number of real octic fields of a prime conductor by
The aim of this paper is to prove the following Theorem Theorem Let be an octic subfield of the field and let be prime. Then divides if and only if divides for some , , , .
On Fleck quotients
On Franel-Kluyver integrals of order three
On Gauss sum characters of finite groups and generalized Bernoulli numbers
On generalized Fibonacci polynomials and Bernoulli numbers.
On Genocchi numbers and polynomials.
On interpolation functions of the generalized twisted -Euler polynomials.
On Krasnér's theorem for the first case of Fermat's last theorem
On mth order Bernoulli polynomials of degree m that are Eisenstein
This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.
On multiple generalized -Genocchi polynomials and their applications.