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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Modular Units (Hardcover, 1981 ed.)
Loot Price: R5,346
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Modular Units (Hardcover, 1981 ed.)
Series: Grundlehren der mathematischen Wissenschaften, 244
Expected to ship within 18 - 22 working days
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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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