相关论文: On Polynomial Time Computable Numbers

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.

We study the number of real zeros of trigonometric polynomials in a period and the number of zeros of self-reciprocal algebraic polynomials on the unit circle under the assumption that their coefficients are in a fixed finite set of real…

In this paper we introduce an applicative theory which characterizes the polynomial hierarchy of time.

The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…

In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-defined analogue to minimal polynomials for a series algebraic…

We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally…

In this article we shows some results about algebra with the group of units having special polynomial identity.

We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.

We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…

A general description of the Vi\`ete coefficients of the gaussian period polynomials is given, in terms of certain symmetric representations of the subgroups and the corresponding quotient groups of the multiplicative group…

Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more…

We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several…

For a polynomial map $\mathbf{f} : k^n \to k^m$ ($k$ a field), we investigate those polynomials $g \in k[t_1,\ldots, t_n]$ that can be written as a composition $g = h \circ \mathbf{f}$, where $h: k^m \to k$ is an arbitrary function. In the…

Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…

"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…

We derive closed formulas for the number of $k$-coloured partitions and the number of plane partitions of $n$ in terms of the Bell polynomials.

In this note we show that groups with definable generics in a separably closed valued of finite imperfection degree can be embedded into groups definable in their algebraic closure.