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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Theory of Jacobi Forms

The Theory of Jacobi Forms

Eichler, Martin
Zagier, Don

Paperback

Series: Progress in Mathematics, Book 55

AlgebraGeneral MathematicsGeometry

ISBN10: 1468491644
ISBN13: 9781468491647
Publisher: Springer Nature
Published: Sep 14 2013
Pages: 150
Weight: 0.64
Height: 0.34 Width: 7.00 Depth: 10.00
Language: English
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.

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