Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalen...Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalent if there exists aninteger matrlx(r s t u)with determinant±1 such that f(x′,y′)=g(x,y),where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
We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether ...We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether a given ideal is prime or prime power. The main algorithm is based on basis representation of finite rings which is computed via Hermite and Smith normal forms.展开更多
文摘Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalent if there exists aninteger matrlx(r s t u)with determinant±1 such that f(x′,y′)=g(x,y),where
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supported by National Natural Science Foundation of China (Grant Nos. 11601202, 11471314 and 11401312)the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 14KJB110012)+1 种基金the High-Level Talent Scientific Research Foundation of Jinling Institute of Technology (Grant No. jit-b-201527)the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
文摘We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether a given ideal is prime or prime power. The main algorithm is based on basis representation of finite rings which is computed via Hermite and Smith normal forms.