In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C[j] in the ...
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In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C[j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q[j] or Z[j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity,that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group.
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Add this copy of Modular Units (Grundlehren Der Mathematischen to cart. $102.16, very good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1981 by Springer.
Add this copy of Modular Units (Volume 244) to cart. $107.20, good condition, Sold by Anybook rated 4.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 1981 by Springer-Verlag.
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Volume 244. This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 900grams, ISBN: 0387905170.
Add this copy of Modular Units to cart. $215.66, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag New York Inc..
Add this copy of Modular Units to cart. $215.66, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1981 by Springer.
Add this copy of Modular Units to cart. $217.69, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2010 by Springer-Verlag New York Inc..
