An elementary treatment of a general diophantine problem
An "exact" formula for the 2n-th Bernoulli number
An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial
We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.
Arithmetic of linear forms involving odd zeta values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.
Arithmetic Subseries of Series with Multiplicative Terms
Arithmetical functions with periodic zeros
Asymptotic Behavior of Some Power Series with ...-functions in the Coefficients.
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Asymptotic expansions of the mean values of Dirichlet L-functions III.
Asymptotic expansions of the mean values of Dirichlet L-functions.
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial.
Basilejský problém devětkrát jinak
V tomto článku podrobně rozebereme celkem devět řešení tzv. basilejského problému (hledání součtu převrácených hodnot druhých mocnin přirozených čísel). První publikované řešení od L. Eulera využívá rozkladu ``nekonečného polynomu'' na součin kořenových činitelů. Druhé řešení pracuje s Taylorovým rozvojem funkce arkussinus a rekurentním vzorcem pro jistý určitý integrál, třetí je založeno na vztazích mezi goniometrickými funkcemi a exponenciálou a výpočtu limity s využitím l'Hospitalova pravidla....
Beiträge zur Theorie der Riemannschen Zetafunktion
Benford's law, values of L-functions and the 3x+1 problem
Borwein and Bradley's Apéry-like formulae for .
Bounding L-functions by class numbers
Bounds for zeta and related functions.
Central binomial sums, multiple Clausen values, and zeta values.
Certain classes of rapidly convergent series representations for L(2n,χ) and L(2n+1,χ)
Chebotarev sets
We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.