A Large Sieve Density Estimate near ?= 1.
A limit theorem for the Hurwitz zeta-function with algebraic irrational parameter.
A limit theorem for the Riemann zeta-function in the complex space
A limit theorem for the Riemann zeta-function near the critical line in the complex space
A Lower Bound for the de Bruijn-Newman Constant ... .
A lower bound for the zeros of Riemann's zeta function on the critical line
A mean square formula for central values of twisted automorphic L-functions
A mean value estimate for real character sums
A mean value theorem for the square of class number times regulator of quadratic extensions
Let be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator for certain families of quadratic extensions of characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions.
A measure-theoretic approach to the invariants of the Selberg class
A motivic Chebotarev density theorem.
A new determinant expression of the zeta function for a hypergraph.
A new irrationality measure for ζ(3)
A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant .
A new lower bound for the de Bruijn-Newman constant.
A note on a formula of van der Pol
A note on arithmetic Diophantine series
We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use simple properties...
A note on certain semigroups of algebraic numbers
The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ ℤ, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic(divisor theory) and analytic(distribution of elements with a given norm) properties of that semigroup and a related semigroup of ideals....
A note on colored Tornheim's double series.
A note on Dirichlet's L-functions