In this paper a kind of theta function is constructed by means of spherical function. And we also obtain some Hilbert modular forms of half integral weight.
A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adi...A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adic modular form.展开更多
Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.
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 give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number.
In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E_8 × E_8 and the Horava-Witten anomaly factorization formula for the gauge group E_8 can be derived through ...In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E_8 × E_8 and the Horava-Witten anomaly factorization formula for the gauge group E_8 can be derived through modular forms of weight 14. This answers a question of Schwarz. We also establish generalizations of these factorization formulas and obtain a new Hoˇrava-Witten type factorization formula.展开更多
In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster de...In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.展开更多
This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the K...This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve.We also explain how to use this family of Kato’s Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve;this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.展开更多
文摘In this paper a kind of theta function is constructed by means of spherical function. And we also obtain some Hilbert modular forms of half integral weight.
基金Supported by the Natural Science Foundation of Peking University
文摘A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adic modular form.
文摘Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.
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.
文摘In this paper we give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number.
基金supported by a start-up grant from National University of Singapore(Grant No.R-146-000-132-133)National Science Foundation of USA(Grant No.DMS-1510216)National Natural Science Foundation of China(Grant No.11221091)
文摘In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E_8 × E_8 and the Horava-Witten anomaly factorization formula for the gauge group E_8 can be derived through modular forms of weight 14. This answers a question of Schwarz. We also establish generalizations of these factorization formulas and obtain a new Hoˇrava-Witten type factorization formula.
基金supported by National Natural Science Foundation of China(Grant No.11901586)the Natural Science Foundation of Guangdong Province(Grant No.2019A1515011323)the Sun Yat-sen University Research Grant for Youth Scholars(Grant No.19lgpy244)。
文摘In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.
基金y the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.20XNLG04)。
文摘This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve.We also explain how to use this family of Kato’s Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve;this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.
