000 02513nam a22004815i 4500
001 978-1-4419-1732-4
003 DE-He213
005 20140220084507.0
007 cr nn 008mamaa
008 100806s2010 xxu| s |||| 0|eng d
020 _a9781441917324
_9978-1-4419-1732-4
024 7 _a10.1007/978-1-4419-1732-4
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
100 1 _aShimura, Goro.
_eauthor.
245 1 0 _aArithmetic of Quadratic Forms
_h[electronic resource] /
_cby Goro Shimura.
250 _a1st.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2010.
300 _aXII, 240p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aThe Quadratic Reciprocity Law -- Arithmetic in an Algebraic Number Field -- Various Basic Theorems -- Algebras Over a Field -- Quadratic Forms -- Deeper Arithmetic of Quadratic Forms -- Quadratic Diophantine Equations.
520 _aThis book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aNumber Theory.
650 2 4 _aGeneral Algebraic Systems.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441917317
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-1732-4
912 _aZDB-2-SMA
999 _c110458
_d110458