The Riemann multiple-space and algebroid functions

Multiple finite Riemann zeta functions

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 function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite cou...

A Lie Algebroid on the Wiener Space

Infinite dimensional Poisson structures play a big role in the theory of infinite dimensional Lie algebras 1 , in the theory of integrable system 2 , and in field theory 3 . But for instance, in 2 , the test functional space where the hydrodynamic Poisson structure acts continuously is not conveniently defined. In 4, 5 we have defined such a test functional space in the case of a linear Poisson...

Riemann Integral of Functions from R into Real Normed Space

Let X be a real normed space, let A be a closed-interval subset of R, let f be a function from A into the carrier of X, and let D be a Division of A. A finite sequence of elements of X is said to be a middle volume of f and D if it satisfies the conditions (Def. 1). (Def. 1)(i) len it = lenD, and (ii) for every natural number i such that i ∈ domD there exists a point c of X such that c ∈ rng(f ...

Unicity Theorem for Algebroid Functions Related to Multiple Values and Derivatives on Annuli

In this paper, we first obtain Xiong inequality of algebroid function on annuli and using this result we prove uniqueness theorem of algebroid functions on annuli concerning to their multiple values and derivative.

The Riemann Zeta and Allied Functions