M.P. Appell's function and vector bundles of rank 2 on elliptic curves

Authors
Citation
A. Polishchuk, M.P. Appell's function and vector bundles of rank 2 on elliptic curves, RAMANUJAN J, 5(2), 2001, pp. 111-128
Citations number
10
Categorie Soggetti
Mathematics
Journal title
RAMANUJAN JOURNAL
ISSN journal
13824090 → ACNP
Volume
5
Issue
2
Year of publication
2001
Pages
111 - 128
Database
ISI
SICI code
1382-4090(2001)5:2<111:MAFAVB>2.0.ZU;2-R
Abstract
This paper is devoted to the function introduced by M.P. Appell in connecti on with decomposition of elliptic functions of the third kind into simple e lements. We show that this function is related to global sections of rank-2 vector bundles on elliptic curves. We derive analogues of theta-identities for this function and prove the divisibility property for the action of th e modular group, that should be considered as a replacement of the function al equation.