Hilbert’s Tenth Problem for Complex Meromorphic Functions in Several Variables
نویسندگان
چکیده
Abstract We prove that Hilbert’s Tenth Problem for meromorphic functions and entire in several variables is unsolvable over the language of rings, together with constant symbols two a predicate place. This first result literature, which proves unsolvability diophantine problem ring complex analytic number variables. The proof rests upon an interplay between geometry, analysis, theory, logic.
منابع مشابه
Difference Picard theorem for meromorphic functions of several variables
It is shown that if n ∈ N, c ∈ C, and three distinct values of a meromorphic function f : C → P of hyper-order ς(f) strictly less than 2/3 have forward invariant pre-images with respect to a translation τ : C → C, τ(z) = z + c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green’s Picard-type theorem in the special case where ς(f) < 2/3, since th...
متن کاملApproximately generalized additive functions in several variables
The goal of this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.
متن کاملSome inequalities in connection to relative orders of entire functions of several complex variables
Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.
متن کاملCircular centered forms for rational functions in several complex variables
Lin, Q. and J.G. Rokne, Circular centered forms for rational functions in several complex variables, Journal of Computational and Applied Mathematics 41 (1992) 347-357. As a continuation of Rokne (this journal, 19871, this paper considers the explicit representation and inclusion properties as well as convergence of circular centered forms for rational complex functions in several variables. !?...
متن کاملAn analogue of Hilbert’s tenth problem for fields of meromorphic functions over non-Archimedean valued fields
Let K be a complete and algebraically closed valued field of characteristic 0. We prove that the set of rational integers is positive existentially definable in the field M of meromorphic functions on K in the language Lz of rings augmented by a constant symbol for the independent variable z and by a symbol for the unary relation “the function x takes the value 0 at 0”. Consequently, we prove t...
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: International Mathematics Research Notices
سال: 2021
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnab185