Just as the function ring case we expect the existence of the coefficient field for the integer ring. Using the notion of one element field in place of such a coefficient field, we calculate absolute… (More)

We consider a generalization of the Mahler measure of a multivariable polynomial P as the integral of log |P | in the unit torus, as opposed to the classical definition with the integral of log |P |.… (More)

In the papers [D1], [D5], [D3] a cohomological formalism for algebraic schemes X0 over spec ZZ or spec Q was conjectured which would explain many of the expected properties of motivic L-series. All… (More)

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our… (More)

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some q-series identity for proving the zeta… (More)

Pairings were first studied as potential attacks on elliptic curve-based cryptography. Recently, protocols have been proposed that make a constructive use of pairings; they require pairing-friendly… (More)

Spectra of real alternating operators seem to be quite interesting from the view point of explaining the Riemann Hypothesis for various zeta functions. Unfortunately we have not sufficient… (More)

We study Ruelle’s type zeta and L-functions for a torsion free abelian group Γ of rank ν ≥ 2 defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta… (More)