Ehrenfels states in the preface to Das Primzahlengesetz that, after a long depression following WWI, the contemplation of the "field of numbers and their eternal, necessary connections" soothed his agonized spirit ("Weltangst") (Ehrenfels 1922, III).
Lately, Carlitz's -Bernoulli numbers have been studied actively by many mathematicians in the field of number theory, discrete mathematics, analysis, mathematical physics, and so on (see [3 18]).
The Euler numbers and polynomials have been studied by researchers in the field of number theory, mathematical physics, and so on (cf. [1, 2, 9, 11, 13 16, 22, 23]).
In the field of number theory and mathematical physics, zeta functions and -functions interpolating these numbers in negative integers have been studied by Cenkci and Can [3], Kim [4 12], and Ozden et al. [16 18].
This approach, which is commonly used in neuroimaging (see e.g., [ 40- 42] for the case of emotion processing) has already been utilized in the field of number processing (e.g., [ 32]).
Recently, M. P. Soler has shown that if a generalized Hilbert space contains any infinite orthonormal set, it must in fact be a classical Hilbert space i.e., the division ring D must be the field of real numbers, the field of complex numbers, or the ring of quaternions.
Landscape was described by its proportion (cover of spring crops, winter crops, woodland, grassland, set-aside) and its structure (number of fields, number of land use types).
Basic notation The symbols,, and denote the ring of integers, the field of rational numbers, and the field of real numbers, respectively.
Throughout this paper,,,,, and will respectively denote the ring of rational integers, the field of rational numbers, the ring -adic rational integers, the field of -adic rational numbers, and the completion of the algebraic closure of.
We denote by (mathbb C) the field of complex numbers.
