Download e-book for iPad: 1969 Number Theory Institute by Lewis D. (ed.)

By Lewis D. (ed.)

ISBN-10: 0821814206

ISBN-13: 9780821814208

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If J(z) E Sk(ro(N'), X) and dN'IN, then J(dz) E Sk(ro(N), X). The forms on Fo(N) which may be obtained in this way from a divisor N' of N (N' =f:. N), span a subspace of Sk(ro(N), X) called the space of oldJorms. Its canonical complement is denoted Skew (ro(N), X) and the eigenforms in this space are called newJorms. 5 The space Sk(H(N), 1) can be decomposed according to the Dirichlet characters X mod N which are the characters of To (N) / H(N): Sk(r1 (N)) = Sk(r1 (N), 1) = EB Sk(ro(N), X)· x The Hecke operators on Sk(rl(N)) respect the above decomposition of this space.

2 The weight distribution of the Melas codes Let q = 2m > 4. Let a be a primitive element ofF q . Let m(x) E F2[X] be the minimal polynomial of a and m_(x) E F2[X] that of a-I. The ideal in the ring F2[X]/(X q- 1 - 1) which is generated by m(x)m_(x) is called a Melas code, and it is denoted by M(q). The definition of the Melas codes is very similar to that of BeH codes. 2) This shows that M(q)1.. and therefore M(q) do not depend on the choice of a up to equivalence. For a description of the weight distribution of M(q) 1..

A curve is called nonsingular or smooth if all the points are nonsingular. In this case, the curve has a tangent at P with equation fx{P)(x - a) for all of its points P = + fy(P)(y - b) =0 (a, b). The definitions for a projective plane curve are similar. From now on, we assume all curves to be smooth and projective.

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1969 Number Theory Institute by Lewis D. (ed.)

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