000			02918nam a22003498i 4500
001			CR9780511752490
003			UkCbUP
005			20200124160239.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100421s1984||||enk o ||1 0|eng|d
020			_a9780511752490 (ebook)
020			_z9780521269834 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA242 _b.M398 1984
082	0	0	_a512/.74 _219
100	1		_aMason, R. C., _eauthor.
245	1	0	_aDiophantine equations over function fields / _cR.C. Mason.
264		1	_aCambridge : _bCambridge University Press, _c1984.
300			_a1 online resource (x, 125 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v96
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520			_aDiophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate.
650		0	_aDiophantine equations.
650		0	_aAlgebraic fields.
776	0	8	_iPrint version: _z9780521269834
830		0	_aLondon Mathematical Society lecture note series ; _v96.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511752490
999			_c518367 _d518365