Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Thanases Pheidas"'
Publikováno v:
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :1625-1636
One of the main open problems regarding decidability of the existential theory of rings is the analogue of Hilbert's Tenth Problem (HTP) for the ring of entire holomorphic functions in one variable. In the direction of a negative solution, we prove u
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bab2efd991edca97c0e794965f8211ae
https://doi.org/10.2422/2036-2145.202010_053
https://doi.org/10.2422/2036-2145.202010_053
Autor:
Thanases Pheidas, Xavier Vidaux
Publikováno v:
International Mathematics Research Notices. 2022:15474-15504
We prove that Hilbert’s Tenth Problem for meromorphic functions and for entire functions in several variables is unsolvable over the language of rings, together with constant symbols for two of the variables and a predicate for a place. This is the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2a175e76e7e36a3fcc639b62dd6f3b41
https://doi.org/10.1093/imrn/rnab185
https://doi.org/10.1093/imrn/rnab185
Autor:
Thanases Pheidas, Xavier Vidaux
Publikováno v:
Journal of the London Mathematical Society. 82:273-278
Buchi's problem asked whether there exists an integer $M$ such that the surface defined by a system of equations of the form $$x_{n}^2+x_{n-2}^2=2x_{n-1}^2+2,\quad n=2,\dotsc, M-1,$$ has no integer points other than those that satisfy $\pm x_n=\pm x_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aac8ecbd1202541ccd6cbeac093a58f
https://doi.org/10.1112/jlms/jdq002
https://doi.org/10.1112/jlms/jdq002
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 17:727-735
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division-ample set of integers and of an elliptic curve of rank one over K). W
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f4cf4674cb0138fbdce9dd4fbd3693b4
https://doi.org/10.5802/jtnb.516
https://doi.org/10.5802/jtnb.516
Autor:
Thanases Pheidas, Xavier Vidaux
Publikováno v:
Fundamenta Mathematicae. 185:171-194
We generalize a question of Buchi: Let R be an integral domain, C a subring and k 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the k th powers of the unknow
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::160fa4b30e5c6f9dc37abd97beed20f4
https://doi.org/10.4064/fm185-2-4
https://doi.org/10.4064/fm185-2-4
Autor:
Karim Zahidi, Thanases Pheidas
Publikováno v:
J. Symbolic Logic 69, iss. 4 (2004), 1006-1026
We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if F is a countable, recursive and perfect field of positive characteristic p, with decidable theory, then the structure of a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb83ca3c1f5d13659e7df0da07f0dbcc
https://doi.org/10.2178/jsl/1102022210
https://doi.org/10.2178/jsl/1102022210
Autor:
Thanases Pheidas
Publikováno v:
Fundamenta Mathematicae. 182:205-220
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::142cac3c68dab7e0af8238a4696bc9f8
https://doi.org/10.4064/fm182-3-2
https://doi.org/10.4064/fm182-3-2
Autor:
Thanases Pheidas, Karim Zahidi
Publikováno v:
Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry. :49-105
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d078300fd7d883510a49720c1369a0b3
https://doi.org/10.1090/conm/270/04369
https://doi.org/10.1090/conm/270/04369
Autor:
Thanases Pheidas
Publikováno v:
Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry. :237-252
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0adaf0babc0694c9e8f67125bd52d0b6
https://doi.org/10.1090/conm/270/04376
https://doi.org/10.1090/conm/270/04376
Autor:
Karim Zahidi, Thanases Pheidas
Publikováno v:
Communications in Algebra. 27:4993-5010
We prove the undecidability of the positive existential theories of: (a) the field C(t), in the language of rings augmented by a constant t and a symbol for the set of derivatives D, D = {x':x ∊ C(t)};(b)any polynomial ring over an integral domain
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec9e054c56dfdb91c229ef80817ce794
https://doi.org/10.1080/00927879908826744
https://doi.org/10.1080/00927879908826744