Integral points of bounded degree on the projective line and in dynamical orbits
نویسندگان
چکیده
منابع مشابه
Integral Points of Fixed Degree and Bounded Height
By Northcott’s Theorem there are only finitely many algebraic points in affine n-space of fixed degree e over a given number field and of height at most X. Finding the asymptotics for these cardinalities as X becomes large is a long standing problem which is solved only for e = 1 by Schanuel, for n = 1 by Masser and Vaaler, and for n “large enough” by Schmidt, Gao, and the author. In this paper...
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Let C ⊂ C1 ×C2 be a curve of type (d1, d2) in the product of the two curves C1 and C2. Let ν be a positive integer. We prove that if a certain inequality involving d1, d2, ν, and the genera of the curves C1, C2, and C is satisfied, then the set of points {P ∈ C(k̄) | [k(P ) : k] ≤ ν} is finite for any number field k. We prove a similar result for integral points of bounded degree on C. These res...
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We study the problem of constructing and enumerating, for any integers m,n > 1, number fields of degree n whose ideal class groups have “large” m-rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
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abstract reception environment has considerable effects on accepting a translation. as the expectations of a target culture and its values and needs change throughout history, its criteria for accepting a translation or rejecting it will change accordingly (gentzler, 2001). the expectations of iran, as the reception environment in the present study, have changed after the islamic revolution. i...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13653