The joint universality and the generalized strong recurrence for Dirichlet L-functions
The Josephus problem
We give explicit non-recursive formulas to compute the Josephus-numbers and and explicit upper and lower bounds for (where ) which differ by (for the bounds are even better). Furthermore we present a new fast algorithm to calculate which is based upon the mentioned bounds.
The jumping champions of the Farey series
The -binomial transforms and the Hankel transform.
The -dimensional Duffin and Schaeffer conjecture
We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.
The Kazandzidis supercongruences. A simple proof and an application
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The k-functions in multiplicative number theory. I. On complex explicit formulae
The k-functions in multiplicative number theory. II. Uniform distribution of zeta zeros
The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
The k-functions in multiplicative number theory. V. Changes of sign of some arithmetical error terms
The Kodaira dimension of certain moduli spaces of abelian surfaces
The Krull-Schmidt theorem for Henselian rings.
The k-tuple jumping champions among consecutive primes
The Kubota symbol for the symplectic group over an imaginary quadratic number field.
The -rank of the real class group of cyclotomic fields
The L2-Lefschetz numbers of Hecke operators.
The l-adic representations attached to a certain noncongruence subgroup.
The Lagrange inversion formula and divisibility properties.