On Siegel Zeros of Hecke-Landau Zeta-Functions.
On simple Igusa local zeta functions.
On the Dirichlet polynomial of finite group of Lie type
On the error term of the mean square formula for the Riemann zeta-function in the critical strip 3/4 < σ < 1
On the exact location of the non-trivial zeros of Riemann's zeta function
We introduce the real valued real analytic function κ(t) implicitly defined by (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.
On the functional properties of Bessel zeta-functions
Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series expansion...
On the k-analogue of a result in the theory of the Riemann zeta function
On the Laurent Coefficients of Certain Dirichlet Series
On the Linnik-Sprindžuk theorem about the zeros of L-functions
On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products
On the Matsumoto zeta-function
On the mean square of the error term for an extended Selberg class
On the mean value of a kind of zeta functions
On the mean value of the generalized Dirichlet -functions
Let be an integer, let denote a Dirichlet character modulo For any real number we define the generalized Dirichlet -functions where with and both real. They can be extended to all by analytic continuation. In this paper we study the mean value properties of the generalized Dirichlet -functions especially for and , and obtain two sharp asymptotic formulas by using the analytic method and the theory of van der Corput.
On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials
On the (non-)contractibility of the order complex of the coset poset of an alternating group
On the order of vanishing of modular -functions at the critical point
On the problem
On the periodicity of trigonometric functions generalized to quotient rings of R[x]
We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.
On the products of Hecke L-functions of holomorphic cusp forms