On a two-variable -adic -function.
On a two-variable zeta function for number fields
This paper studies a two-variable zeta function attached to an algebraic number field , introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov divisors. When this function becomes the completed Dedekind zeta function of the field . The function is a meromorphic function of two complex variables with polar divisor , and it satisfies the functional equation . We consider the special case , where for this function...
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 an Effective Order Estimate of the Riemann Zeta Function in the Critical Strip.
On an identity between infinite series of arithmetic functions
On Artin's conjecture.
On Cantor's singular moments.
On certain character sums
On Certain Dirichlet Series Associated with Hilbert Modular Forms and Rankin's Method.
On Certain Dirichlet Series Whose Coefficients Are Related to Class Numbers.
On certain Euler products
On certain infinite products III
On certain sums over ordinates of zeta-zeros
On character sums and the non-vanishing for s > 0 of Dirichlet L-series belonging to real odd characters χ
On characterization of Dirichlet L-functions
On Cramér's theorem for general Euler products with functional equation.
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.