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ON THETA FUNCTIONS OF ORDER FOUR
, 810
"... Abstract. We prove that the fourth powers of theta functions with even characteristics form a basis of the space H 0 (A, OA(4ϑ))+ of even theta functions of order four on a principally polarized Abelian variety (A, ϑ) without vanishing thetanull. 1. ..."
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Abstract. We prove that the fourth powers of theta functions with even characteristics form a basis of the space H 0 (A, OA(4ϑ))+ of even theta functions of order four on a principally polarized Abelian variety (A, ϑ) without vanishing thetanull. 1.
Harmonic Theta Functions . . .
"... The introduction contains an historical survey of the transformation theory of theta functions and theta series of integral quadratic forms under Hecke operators. In the main part the explicit formulas are deduced which express images under Hecke operators of general vectorvalued theta functions w ..."
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The introduction contains an historical survey of the transformation theory of theta functions and theta series of integral quadratic forms under Hecke operators. In the main part the explicit formulas are deduced which express images under Hecke operators of general vectorvalued theta functions
Transformation Laws for Theta Functions
 Rocky Mount. J. Math
, 2004
"... ABSTRACT. We determine transformation laws for theta functions of higher degree. 1. Introduction. Siegel [8 10], for example, proves transformation laws for theta functions (depending on a single complex variable) attached to quadratic forms. If the quadratic form is indefinite, then Siegel’s defin ..."
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Cited by 4 (2 self)
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ABSTRACT. We determine transformation laws for theta functions of higher degree. 1. Introduction. Siegel [8 10], for example, proves transformation laws for theta functions (depending on a single complex variable) attached to quadratic forms. If the quadratic form is indefinite, then Siegel’s
A theta function for hyperbolic . . .
, 2008
"... For a Riemann surface with cusps we define a theta function using the eigenvalues of the Laplacian and the singularities of the scattering determinant. We provide its meromorphic continuation and discuss its singularities. ..."
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For a Riemann surface with cusps we define a theta function using the eigenvalues of the Laplacian and the singularities of the scattering determinant. We provide its meromorphic continuation and discuss its singularities.
The product of partial theta functions
 Adv. Appl. Math
"... Abstract. In this paper, we prove a new identity for the product of two partial theta functions. An immediate corollary is Warnaar’s generalization of the Jacobi triple product identity. 1. ..."
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Cited by 6 (0 self)
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Abstract. In this paper, we prove a new identity for the product of two partial theta functions. An immediate corollary is Warnaar’s generalization of the Jacobi triple product identity. 1.
Computing Riemann theta functions
, 2003
"... The Riemann theta function is a complexvalued function of g complex variables. It appears in the construction of many (quasi)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise ..."
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Cited by 9 (3 self)
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The Riemann theta function is a complexvalued function of g complex variables. It appears in the construction of many (quasi)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing
Mock (false) theta functions as . . .
, 2005
"... We establish a correspondence between the SU(2) Witten–Reshetikhin–Turaev invariant for the Seifert manifold M(p1, p2, p3) and Ramanujan’s mock theta functions. ..."
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We establish a correspondence between the SU(2) Witten–Reshetikhin–Turaev invariant for the Seifert manifold M(p1, p2, p3) and Ramanujan’s mock theta functions.
Lagrangian fibrations and theta functions
, 2006
"... In this thesis we study asymptotic behavior of projective embeddings of abelian varieties and their amoebas. The projective embeddings are given by theta functions. It is known that a Lagrangian fibration of the abelian variety determines a basis of theta functions. After reviewing the relation from ..."
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In this thesis we study asymptotic behavior of projective embeddings of abelian varieties and their amoebas. The projective embeddings are given by theta functions. It is known that a Lagrangian fibration of the abelian variety determines a basis of theta functions. After reviewing the relation
Quantization and “theta functions”
, 1999
"... Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how this treatment can be used to construct a special basis in every space of conformal blocks. This is a direct generalization of the basis of ..."
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of theta functions with characteristics in every complete linear system on an Abelian variety (see [Mum]). The same construction generalizes the classical theory of theta functions to vector bundles of higher rank on Abelian varieties and K3 surfaces. We also discuss the geometry behind these constructions
Tropical curves, their Jacobians and theta functions
, 2006
"... We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the AbelJacobi, RiemannRoch and Riemann theta divisor theorems. ..."
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Cited by 92 (4 self)
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We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the AbelJacobi, RiemannRoch and Riemann theta divisor theorems.
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115,303