Elliptic modular functions and elliptic genera

Trigonometric functions, elliptic functions, elliptic modular forms

Liouville Field, Modular Forms and Elliptic Genera

When we describe non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix under modular transformations and do not have good modular properties. In this article we propose a method of combining discrete and continuous representations so that they have good modular behavior and can be used as conformal blo...

On Elliptic Genera and Theta-Functions

The main purpose of this paper is to give a simple and unified new proof of the Witten rigidity theorems, which were conjectured by Witten and first proved by Taubes [T], Bott-Taubes [BT], Hirzebruch [H] and Krichever [Kr]. Our proof shows that the modular invariance, which is the intrinsic symmetry of elliptic genera, actually implies their rigidity. Some new properties of elliptic genera and ...

Partition functions and elliptic genera from supergravity

We develop the spacetime aspects of the computation of partition functions for string/M-theory on AdS3 × M . Subleading corrections to the semi-classical result are included systematically, laying the groundwork for comparison with CFT partition functions via the AdS3/CFT2 correspondence. This leads to a better understanding of the “Farey tail” expansion of Dijkgraaf et. al. from the point of v...

Introducing elliptic, an R package for elliptic and modular functions

This paper introduces the elliptic package of R routines, for numerical calculation of elliptic and related functions. Elliptic functions furnish interesting and instructive examples of many ideas of complex analysis, and package elliptic illustrates these numerically and visually. A statistical application in fluid mechanics is presented. An earlier version of this vignette was published as Ha...