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The Theory of Jacobi Forms (Paperback, 1985 ed.)
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The Theory of Jacobi Forms (Paperback, 1985 ed.)
Series: Progress in Mathematics, 55
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The functions studied in this monogra9h are a cross between
elliptic functions and modular forms in one variable. Specifically,
we define a Jacobi form on SL (~) to be a holomorphic function 2
(JC = upper half-plane) satisfying the t\-10 transformation
eouations 2Tiimcz* k CT +d a-r +b z ) (1) ( (cT+d) e cp(T,z) cp CT
+d ' CT +d (2) rjl(T, z+h+]l) and having a Four*ier expansion of
the form 00 e2Tii(nT +rz) (3) cp(T,z) 2: c(n,r) 2:: rE~ n=O 2 r ~
4nm Here k and m are natural numbers, called the weight and index
of rp, respectively. Note that th e function cp (T, 0) is an
ordinary modular formofweight k, whileforfixed T thefunction
z-+rjl(-r,z) isa function of the type normally used to embed the
elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp
is independent of z and the definition reduces to the usual notion
of modular forms in one variable. We give three other examples of
situations where functions satisfying (1)-(3) arise classically: 1.
Theta series. Let Q: ~-+ ~ be a positive definite integer valued
quadratic form and B the associated bilinear form.
General
Imprint: |
Birkhauser Boston
|
Country of origin: |
United States |
Series: |
Progress in Mathematics, 55 |
Release date: |
September 2014 |
First published: |
1985 |
Authors: |
Martin Eichler
• Don Zagier
|
Dimensions: |
254 x 178 x 9mm (L x W x T) |
Format: |
Paperback
|
Pages: |
150 |
Edition: |
1985 ed. |
ISBN-13: |
978-1-4684-9164-7 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
1-4684-9164-4 |
Barcode: |
9781468491647 |
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