On higher genus Weierstrass sigma-function

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0


to be published in Physica D

Scientific paper

The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces. Our definition of the odd higher genus sigma-function is based on a generalization of the classical representation of the elliptic sigma-function via Jacobi theta-function. Namely, the odd higher genus sigma-function $\sigma_{\chi}(u)$ (for $u\in \C^g$) is defined as a product of the theta-function with odd half-integer characteristic $\beta^{\chi}$, associated with a spin line bundle $\chi$, an exponent of a certain bilinear form, the determinant of a period matrix and a power of the product of all even theta-constants which are non-vanishing on a given Riemann surface. We also define an even sigma-function corresponding to an arbitrary even spin structure. Even sigma-functions are constructed as a straightforward analog of a classical formula relating even and odd sigma-functions. In higher genus the even sigma-functions are well-defined on the moduli space of Riemann surfaces outside of a subspace defined by vanishing of the corresponding even theta-constant.

No associations


Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.


On higher genus Weierstrass sigma-function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On higher genus Weierstrass sigma-function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On higher genus Weierstrass sigma-function will most certainly appreciate the feedback.

Rate now


Profile ID: LFWR-SCP-O-253535

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.