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.