Open AccessPrime forms and higher genus deformed Eisenstein series
Author(s) -
Alexander Zuevsky
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1416/1/012044
Subject(s) - eisenstein series , mathematics , genus , prime (order theory) , riemann surface , pure mathematics , kernel (algebra) , vertex (graph theory) , algebra over a field , computation , number theory , combinatorics , algorithm , botany , graph , modular form , biology
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.