Related papers: A panorama on zeta functions
The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold…
We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map…
We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for {\zeta}(s). We present here, after showing the first proof of Riemann, a new, simple and direct proof of…
The aim of this paper is to show how zeta functions and excision in cyclic cohomology may be combined to obtain index theorems. In the first part, we obtain a local index formula for "abstract elliptic pseudodifferential operators"…
We study some of the interactions between the Fourier Transform and the Riemann zeta function (and Dirichlet-Dedekind-Hecke-Tate L-functions)
For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…
We introduce a screw function corresponding to the Riemann zeta-function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them…
In this paper, we give a more direct proof of the results by Clair and Mokhtari-Sharghi on the zeta functions of periodic graphs. In particular, using appropriate operator-algebraic techniques, we establish a determinant formula in this…
We define a new weighted zeta function for a finite digraph and obtain its determinant expression called the Ihara expression. The graph zeta function is a generalization of the weighted graph zeta function introduced in previous research.…
We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.
The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.
Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, in the study of multiple zeta functions…
We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and negative integer arguments are respectively multiple zeta values and poly-Bernoulli…
For these two decades, the Arakawa-Kaneko zeta function has been studied actively. Recently Kaneko and Tsumura constructed its variants from the viewpoint of poly-Bernoulli numbers. In this paper, we generalize their zeta functions of…
The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series which involves a product of Riemann zeta-functions of a special form.
We give an overview of the theory of functional relations for zeta-functions of root systems, and show some new results on functional relations involving zeta-functions of root systems of types $B_r$, $D_r$, $A_3$ and $C_2$. To show those…
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
We obtain several expansions for $\zeta(s)$ involving a sequence of polynomials in $s$, denoted in this paper by $\alpha_k(s)$. These polynomials can be regarded as a generalization of Stirling numbers of the first kind and our identities…