000 03450nam a22003858i 4500
001 CR9780511542893
003 UkCbUP
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006 m|||||o||d||||||||
007 cr||||||||||||
008 090505s2005||||enk o ||1 0|eng|d
020 _a9780511542893 (ebook)
020 _z9780521605830 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA242
_b.D28 2005
082 0 0 _a512.7/4
_222
100 1 _aDavenport, Harold,
_d1907-1969,
_eauthor.
245 1 0 _aAnalytic methods for Diophantine equations and Diophantine inequalities /
_cH. Davenport.
246 3 _aAnalytic Methods for Diophantine Equations & Diophantine Inequalities
264 1 _aCambridge :
_bCambridge University Press,
_c2005.
300 _a1 online resource (xx, 140 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge mathematical library
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _tWaring's problem /
_rR. C. Vaughan --
_tForms in many variables /
_rD. R. Heath-Brown --
_tDiophantine inequalities /
_rD. E. Freeman --
_g1.
_tIntroduction --
_g2.
_tWaring's problem : history --
_g3.
_tWeyl's inequality and Hua's inequality --
_g4.
_tWaring's problem : the asymptotic formula --
_g5.
_tWaring's problem : the singular series --
_g6.
_tsingular series continued --
_g7.
_tequation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N --
_g8.
_tequation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 --
_g9.
_tWaring's problem : the number G(k) --
_g10.
_tequation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again --
_g11.
_tGeneral homogeneous equations : Birch's theorem --
_g12.
_tgeometry of numbers --
_g13.
_tCubic forms --
_g14.
_tCubic forms : bilinear equations --
_g15.
_tCubic forms : minor arcs and major arcs --
_g16.
_tCubic forms : the singular integral --
_g17.
_tCubic forms : the singular series --
_g18.
_tCubic forms : the p-adic problem --
_g19.
_tHomogeneous equations of higher degree --
_g20.
_tDiophantine inequality.
520 _aHarold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.
650 0 _aDiophantine analysis.
650 0 _aDiophantine equations.
700 1 _aBrowning, Tim,
_eauthor.
776 0 8 _iPrint version:
_z9780521605830
830 0 _aCambridge mathematical library.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511542893
999 _c517789
_d517787