scholarly journals Counting solvable $S$-unit equations

2021 ◽  
pp. 1
Author(s):  
I. E. Shparlinski ◽  
C. L. Stewart
Keyword(s):  
Unit Equations

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

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

scholarly journals Bounds for the solutions of unit equations

1996 ◽  
Vol 74 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Yann Bugeaud ◽  
Kálmán Győry
Keyword(s):  
Unit Equations

scholarly journals S-unit equations and their applications

1988 ◽  
pp. 110-174 ◽  
Author(s):  
J.-H. Evertse ◽  
K. Győry ◽  
C. L. Stewart ◽  
R. Tijdeman
Keyword(s):  
Unit Equations

scholarly journals Additive relations in fields

1991 ◽  
Vol 51 (1) ◽  
pp. 154-170 ◽  
Author(s):  
A. J. Van Der Poorten ◽  
H. P. Schlickewei
Keyword(s):  
Characteristic Zero ◽  
Number Fields ◽  
Growth Conditions ◽  
Number Of Solutions ◽  
Unit Equations ◽  
Recurrence Sequences

AbstractThis paper is the first part of a long delayed revision of the manuscript ‘The growth conditions recurrence sequences’ (circulated in 1982) in which the authors outlined a proof of the now well known theorem on the finiteness of the number of solutions of S-unit equations. The argument lifting the result from number fields to arbitrary fields of characteristic zero has original features.

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