Abstract The Riemann zeta distribution, defined as the one whose characteristic function is the normalised Riemann zeta function, is an interesting example of an infinitely divisible distribution. The infinite divisibility of the distribution has been proved with recourse to the Euler product of the Riemann zeta function. In this paper, we look at multiple zeta-star function, which is a multi-d...

Abstract. In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher’s identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting formulas related to values of the Hurwitz zeta function. We also get an extension of the bivariate identity of Cohen to values of the Hurwitz zeta fu...

Given an abelian Galois extension K/F of number fields, a quaternion algebra A over F that is ramified at all infinite primes, and a character χ of the Galois group of K over F , we consider the twist of the zeta function of A by the character χ. We show that such twisted zeta functions provide a factorization of the zeta function of A(K) = A ⊗F K. Also, the quotient of the zeta function for A(...

Stark and Terras introduced the edge zeta function of a finite graph in 1996. The edge zeta function is the reciprocal of a polynomial in twice as many variables as edges in the graph and can be computed in polynomial time. We look at graph properties which we can determine using the edge zeta function. In particular, the edge zeta function is enough to deduce the clique number, the number of H...

Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety defined over a finite field. We then explain two approaches to the general structural properties of the partial zeta function in the direction of the Weil type conjectures. The first approach, using an inductive fibred variety point of vi...

The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negati...

روش‌های مختلفی برای زمان­‌سنجی امواج مشابه و با تحریک یکسان ارایه شده است که توجه به شرایط موج می‌­توان بهترین گزینه را انتخاب کرد. لذا هدف ما یافتن روش زمان‌سنجی جهت خروجی از حسگر UFSD زیرا می­‌خواستیم این حسگرها آشکارسازی پروتون‌ها در سیستم پروتون درمانی برای­ درمان ­تومورهای سرطانی استفاده کنیم. راستا مقایسه مختلف مثل تفکیک‌کننده کسر ثابت (CFD)، همبستگی متقابل(CC) زمان بیش آستانه (TOT)با داد...

These notes are a rather subjective account of the theory of dynamical zeta functions. They correspond to three lectures presented by the author at the “Numeration” meeting in Leiden in 2010. 1 A Selection of Zeta Functions In its various manifestations, a zeta function ζ(s) is usually a function of a complex variable s ∈ C. We will concentrate on three main types of zeta function, arising in t...

We compute explicitly the normal zeta functions of the Heisenberg groups H(R), where R is a compact discrete valuation ring of characteristic zero. These zeta functions occur as Euler factors of normal zeta functions of Heisenberg groups of the form H(OK), where OK is the ring of integers of an arbitrary number field K, at the rational primes which are non-split in K. We show that these local z...