| The Theory of Jacobi Forms 1985 Edition Contributor(s): Eichler, Martin (Author), Zagier, Don (Author) |
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ISBN: 1468491644 ISBN-13: 9781468491647 Publisher: Birkhauser OUR PRICE: $123.49 Product Type: Paperback Published: September 2013 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Geometry - Algebraic - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| Series: Progress in Mathematics |
| Physical Information: 0.34" H x 7" W x 10" (0.64 lbs) 150 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |