On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
On a relation between the Riemann zeta function and the Stirling numbers.
On an Approximate Functional Equation for Dirichlet L-Series.
On an asymptotic formula of Ramanujan for a certain theta-type series
On an asymptotic formula of Srinivasa Ramanujan
On Certain Dirichlet Series Whose Coefficients Are Related to Class Numbers.
On certain sums over ordinates of zeta-zeros
On critical values of twisted Artin -functions
We give a simple proof that critical values of any Artin -function attached to a representation with character are stable under twisting by a totally even character , up to the -th power of the Gauss sum related to and an element in the field generated by the values of and over . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.
On Dirchlet's series satisfying Riemann's functional equation.
On discrete mean values of Dirichlet -functions
Let be a nonprincipal Dirichlet character modulo a prime number and let . Define the mean value We give an identity for which, in particular, shows that for fixed and .
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function.
On gigantic density of zeros of some signals defined by prime numbers
On higher-power moments of E(t)
On higher-power moments of Δ(x)
On higher-power moments of Δ(x) (II)
On higher-power moments of Δ(x) (III)
On hypergeometric-type generating relations associated with the generalized zeta function.
On Karatsuba Conjecture and the Lindelöf Hypothesis
On Kronecker's limit formula for Dirichlet series with periodic coefficients
On large values of the Riemann zeta-function on short segments of the critical line
We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.