000			02021nam a2200277Ia 4500
003			OSt
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008			231229s9999 xx 000 0 und d
020			_a9780387900407
040			_cIISER BPR
041			_aEng
082			_a512.944 _bSER _223rd
100			_aSerre, Jean-Pierre
245		2	_aCourse in arithmetic
250			_a1st ed.
260			_aNew York: _bSpringer-Verlag, _cc1973.
300			_aix, 118p. : _bill (hb). ; _c22cm.
440			_aGraduate texts in mathematics ; _vVol. 7
520			_aThis book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor­ phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors. Includes bibliography, index of definitions and index of notations.
650			_aMathematics
650			_aAlgebra
650			_aAnalytic methods
942			_cBK _2ddc
947			_a5262.136831
948			_a0.22
999			_c3184 _d3184