49 research outputs found
Identities on the k-ary Lyndon words related to a family of zeta functions
The main aim of this paper is to investigate and introduce relations between
the numbers of k-ary Lyndon words and unified zeta-type functions which was
defined by Ozden et al [15, p. 2785]. Finally, we give some identities on
generating functions for the numbers of k-ary Lyndon words and some special
numbers and polynomials such as the Apostol-Bernoulli numbers and polynomials,
Frobenius-Euler numbers, Euler numbers and Bernoulli numbers.Comment: 9 page
Some New Symmetric Identities for the q-Zeta Type Functions
The main object of this paper is to obtain several symmetric properties of
the q-Zeta type functions. As applications of these properties, we give some
new interesting identities for the modified q-Genocchi polynomials. Finally,
our applications are shown to lead to a number of interesting results which we
state in the present paper.Comment: 8 pages; submitte
Nonstandard Mathematics and New Zeta and L-Functions
This Ph.D. thesis, prepared under the supervision of Professor Ivan Fesenko,
defines new zeta functions in a nonstandard setting and their analytical
properties are developed. Further, p-adic interpolation is presented within a
nonstandard setting which enables the concept of interpolating with respect to
two, or more, distinct primes to be defined.
The final part of the dissertation examines the work of M. J. Shai Haran and
makes initial attempts of viewing it from a nonstandard perspective.Comment: Ph.D. Thesis, University of Nottingham, 2007, 163 page