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Könyv The Theory of Jacobi Forms Martin Eichler

The Theory of Jacobi Forms

Szerző: Martin Eichler, Don Zagier
Nyelv: Angol
Kötés: Puha kötésű
Kiadó: Springer, Berlin
Elérhetőség: Beszállítói készleten
Küldés 5-8 napon belül
43 610 Ft
The functions studied in this monogra9h are a cross between elliptic functions and modular forms in...

Információk a könyvről

Szerző
Martin Eichler, Don Zagier
Nyelv
Angol
Kötés
Könyv - Puha kötésű
Kiadva
2013
oldal
150
EAN
9781468491647
ISBN
1468491644
Enbook ID
05258300
Kiadó
Springer, Berlin
Súly
316
Méretek
178 x 254 x 9

Teljes leírás

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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