MODULAR FORMS-page5 - in R 2 i.e a free subgroup of rank 2...

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Lecture 1 Binary Quadratic Forms 1.1 The theory of modular form originates from the work of C.F. Gauss of 1831 in which he gave a geometrical interpretation of some basic notions of number theory. Let us start with choosing two non-proportional vectors in R 2 v = ( a, b ) , w = ( c, d ) . The set of vectors Λ = Z v + Z w := { m 1 v + m 2 w R 2 | m 1 , m 2 Z } forms a
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Unformatted text preview: in R 2 , i.e., a free subgroup of rank 2 of the additive group of the vector space R 2 . We picture it as follows: Fig.1 The area A ( v , w ) of the parallelogram formed by the vectors v and w is given by the formula A ( v , w ) 2 = det ± v · v v · w v · w w · w ² . 1...
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