Indefinite theta series of signature (1,1) from the point of view of homological mirror symmetry

Details Indefinite theta series of signature (1,1) from the point of view of homological mirror symmetry Indefinite theta series of signature (1,1) from the point of view of homological mirror symmetry

2000-03-13

arxiv.org/abs/math/0003076v3

Mathematics

Algebraic Geometry

37 pages, minor structural changes

Scientific paper

We apply the homological mirror symmetry for elliptic curves to the study of indefinite theta series. We prove that every such series corresponding to a quadratic form of signature (1,1) can be expressed in terms of theta series associated with split quadratic forms and the usual theta series. We also show that indefinite theta series corresponding to univalued Massey products between line bundles on elliptic curve are modular.

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