Prime forms and higher genus deformed Eisenstein series

0521943 - MÚ 2020 RIV GB eng C - Conference Paper (international conference)
Zuevsky, Alexander
Prime forms and higher genus deformed Eisenstein series.
Journal of Physics: Conference series. Vol. 1416. Bristol: IOP, 2019 - (Burdík, Č.; Navrátil, O.; Pošta, S.), č. článku 012044. ISSN 1742-6588.
[International Conference on Integrable Systems and Quantum Symmetries (ISQS-26) /26./. Prague (CZ), 08.07.2019-12.07.2019]
R&D Projects: GA ČR(CZ) GA18-00496S
Institutional support: RVO:67985840
Keywords : complex spheres * recurrent formulae * Riemann surfaces * Theta-function
OECD category: Pure mathematics
https://iopscience.iop.org/article/10.1088/1742-6596/1416/1/012044

Using the theory of Szegő kernel on a genus g Riemann surfaces obtained as a result of the multiple ρ-parameter formalism of sewing of g handles to the complex sphere, we derive new formulas related prime forms, theta functions, and deformed Eisenstein series. We establish recurrent formulas for genus g prime forms and Szegő kernel as well as further identities. Using the above results, we introduce finally another definition of genus g counterpart of genus one deformed Eisenstein series. The results obtained are then useful in computation of vertex algebra related cohomologies.
Permanent Link: http://hdl.handle.net/11104/0306490