scholarly journals Bounds for the solutions of $S$-unit equations and decomposable form equations II.

2019 ◽  
Vol 94 (3-4) ◽  
pp. 507-526
Author(s):  
Kalman Gyory
Keyword(s):  
Unit Equations ◽  
Decomposable Form

scholarly journals Bounds for the solutions of S-unit equations and decomposable form equations

2006 ◽  
Vol 123 (1) ◽  
pp. 9-41 ◽  
Author(s):  
Kálmán Győry ◽  
Kunrui Yu
Keyword(s):  
Unit Equations ◽  
Decomposable Form

scholarly journals Determining the small solutions to $S$-unit equations

1999 ◽  
Vol 68 (228) ◽  
pp. 1687-1700 ◽  
Author(s):  
N. P. Smart
Keyword(s):  
Unit Equations

scholarly journals One-parameter families of unit equations

2006 ◽  
Vol 13 (6) ◽  
pp. 935-945 ◽  
Author(s):  
Aaron Levin
Keyword(s):  
Unit Equations

scholarly journals Two S-unit equations with many solutions

2007 ◽  
Vol 124 (1) ◽  
pp. 193-199 ◽  
Author(s):  
S. Konyagin ◽  
K. Soundararajan
Keyword(s):  
Unit Equations

scholarly journals Decomposable form equations

2015 ◽  
pp. 231-283
Author(s):  
Jan-Hendrik Evertse ◽  
Kalman Gyory
Keyword(s):  
Decomposable Form

Unit equations in several unknowns

2015 ◽  
pp. 128-172
Author(s):  
Jan-Hendrik Evertse ◽  
Kalman Gyory
Keyword(s):  
Unit Equations

scholarly journals Effective results for unit points on curves over finitely generated domains

2015 ◽  
Vol 158 (2) ◽  
pp. 331-353
Author(s):  
ATTILA BÉRCZES
Keyword(s):  
Algebraic Closure ◽  
Unit Group ◽  
Number Fields ◽  
Finitely Generated ◽  
Quotient Field ◽  
Effective Version ◽  
Formula Group ◽  
Commutative Domain ◽  
Image Position ◽  
Unit Equations

AbstractLet A be a commutative domain of characteristic 0 which is finitely generated over ℤ as a ℤ-algebra. Denote by A* the unit group of A and by K the algebraic closure of the quotient field K of A. We shall prove effective finiteness results for the elements of the set \begin{equation*} \mathcal{C}:=\{ (x,y)\in (A^*)^2 | F(x,y)=0 \} \end{equation*} where F(X, Y) is a non-constant polynomial with coefficients in A which is not divisible over K by any polynomial of the form XmYn - α or Xm - α Yn, with m, n ∈ ℤ⩾0, max(m, n) > 0, α ∈ K*. This result is a common generalisation of effective results of Evertse and Győry [12] on S-unit equations over finitely generated domains, of Bombieri and Gubler [5] on the equation F(x, y) = 0 over S-units of number fields, and it is an effective version of Lang's general but ineffective theorem [20] on this equation over finitely generated domains. The conditions that A is finitely generated and F is not divisible by any polynomial of the above type are essentially necessary.

scholarly journals Group Topologies on the Integers and S-Unit Equations

2020 ◽  
Vol 61 (3) ◽  
pp. 542-544
Author(s):  
S. V. Skresanov
Keyword(s):  
Unit Equations
Sign in / Sign up

Export Citation Format

Share Document