A. Robert - Elliptic Curves
Published: 1986-02-01 | ISBN: 0387063099, 3540063099 | PDF | 264 pages | 10 MB
We have used the usual letters for the basic sets of numbers N (natural integers 0,1,2, ... ), ~ (ring of rational integers), ~ (field of rational numbers), R (field of real numbers), [ (field of complex numbers), Fq (finite field with q elements). As a rule, we denote by AX the multiplicative group of units (invertible elements) in a ring A. In formulas, the cypher 1 always represents the number one (except in log x ... so that in one occurence I have used log to avoid ambiguities). Also ~(x) =e 2rrix (normalized exponential). In a theorem, I list properties under Latin letters a), b), ... keeping i), ii), ... for equivalent properties, but the meaning is always clear by the context. The following system has been adopted for cross-references. All theorems, propositions, corollaries, lemmas, remarks, definitions, formulas, errata, ... are numbered in one sequence. Such a cypher as (nL3.4) refers to the item (3.4) of chapter III, i.e. the fourth numbered in section 3. (This happens to be a lemma 3.J" From inside chapter III we would refer to (3.4) (in section 3, sometimes simply to lemma 3 this last system of numeration has not been used systematically, but only when it can be more suggestive locally).
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