Theta functions for indefinite polarizations
نویسندگان
چکیده
منابع مشابه
Theta Functions for Indefinite Polarizations
We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective) flat connection on this family coming from a heat operator. They also possess modular properties similar to the classical ones.
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The purpose of this paper is to use indefinite theta functions to explain and generalize an example of a Maass waveform which was constructed by Cohen from two functions σ and σ∗, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are “nearly” Maass waveforms. In certain special cases we obtain act...
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We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.
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Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ mock theta functions of type ( p, 1) as line integrals in hyperbolic p-space.
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where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2004
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2004.065