Effective Hilbert's irreducibility theorem for global fields

被引:1
作者
Paredes, Marcelo [1 ]
Sasyk, Roman [2 ,3 ]
机构
[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Pabellon 1,Ciudad Univ, RA-1428 Buenos Aires, Argentina
[2] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat Alberto P Calderon, Saavedra 15,Piso 3, RA-1083 Buenos Aires, Argentina
[3] Univ Buenos Aires, Fac Ingn, Dept Matemat, Ave Paseo Colon 850, RA-1063 Buenos Aires, Argentina
关键词
RATIONAL-POINTS; CONJECTURE; BOUNDS; CURVES; NUMBER;
D O I
10.1007/s11856-023-2604-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove an effective form of Hilbert's irreducibility theorem for polynomials over a global field K. More precisely, we give effective bounds for the number of specializations t is an element of O-K that do not preserve the irreducibility or the Galois group of a given irreducible polynomial F(T, Y) is an element of K[T, Y]. The bounds are explicit in the height and degree of the polynomial F(T, Y), and are optimal in terms of the size of the parameter t is an element of O-K. Our proofs deal with the function field and number field cases in a unified way.
引用
收藏
页码:851 / 877
页数:27
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