Algebraic guides to transcendental problems
نویسندگان
چکیده
منابع مشابه
Algebraic and Transcendental Numbers
To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...
متن کاملAlgebraic Dynamics and Transcendental Numbers
A first example of a connection between transcendental numbers and complex dynamics is the following. Let p and q be polynomials with complex coefficients of the same degree. A classical result of Böttcher states that p and q are locally conjugates in a neighborhood of∞: there exists a function f , conformal in a neighborhood of infinity, such that f(p(z)) = q(f(z)). Under suitable assumptions,...
متن کاملDeciding polynomial-transcendental problems
This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans(x) in which the variables range over the real numbers. The list of transcendental functions to which our decision method directly applies includes exp(x), the exponential function with respect to base e, ln(x)...
متن کاملAlgebraic Values of Transcendental Functions at Algebraic Points
In this paper, the authors will prove that any subset of Q can be the exceptional set of some transcendental entire function. Furthermore, we could generate this theorem to a much more general version and present a unified proof.
متن کاملA Transcendental Method in Algebraic Geometry
It is well known that the basic objects of algebraic geometry, the smooth projective varieties, depend continuously on parameters as well as having the usual discrete invariants such as homotopy and homology groups. What I shall attempt here is to outline a procedure for measuring this continuous variation of structure. This method uses the periods of suitably defined rational differential form...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1922
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1922-03544-6