title: Rational Points on Curves over Finite Fields: Theory and Applications (London Mathematical Society Lecture Note Series)
author:  Harald Niederreiter 
description: '... the book under review develops many techniques that are not covered in the existing texts. I highly recommend it.' Steven D. Galbraith, Royal Holloway, University of London<br /><br />'Because of the carefully selected contents and lucid style, the book can be warmly recommended to mathematicians interested in the above-mentioned topics or in algebraic curves over finite fields with many rational points.' EMS<br /><br />'The book is very clearly written. It is warmly recommended to anyone who is interested in nice mathematical theories and/or in the recent applications.' Acta. Sci. Math.
zlib_text: 111
  Sémz’naz‘re de Théorz'e des Nombres
  Paris 1986-87
  Higher regulators of elliptic curves with cornk lex multiplication
  Christopher DENINGER<
  Introduction :
  In [5], [6] Bloch has given a
  K—theoretical interpretation up to a nonzero
  rational multiple for the value L(E,2) of the L—series of an elliptic curve E Over
  Q
  with complex multiplication. His ideas have been extended by Beilinson to very
  general conjectures about
  an arithmetic geometric interpretation of values of
  L—series
  L(H1(X),s)
  of smooth projective varieties
  X
  over number fields [2].
  Using the (conjectural) functional equation they say that up to a non—vanishing
  rational number the leading coefficient of such an
  L—series at an integer left from
  é—
  is equal to a certain generalized regulator determinant. This determinant is
  obtained by comparing two
  Q—structures on real Deligne cohomology
  :
  one
  obtained from algebraic
  K—theory the other obtained from the deRham—Betti
  cohomologies of the variety [2], [13], [14]. In [3] Beilin