We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed...We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.展开更多
In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta funct...In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan＇s identities, Winquist＇s identity and many other interesting identities.展开更多
The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction wil...The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction will be made in the present article.展开更多
In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k ...In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k = k（q） = r（q）r2 （q2）.展开更多
文摘We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.
基金Supported by Innovation Program of Shanghai Municipal Education Commission and PCSIRT
文摘In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan＇s identities, Winquist＇s identity and many other interesting identities.
文摘The importance of basic hypergeometric series has been widely recognized. For non specialists, it is necessary to have a quick introduction to this classical but flourishing subject. An effort along this direction will be made in the present article.
文摘In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k = k（q） = r（q）r2 （q2）.
