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Representation of Numbers by Binary Quadratic Forms
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作者 李德琅 《Acta Mathematica Sinica,English Series》 SCIE 1987年第1期58-65,共8页
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
关键词 representation of Numbers by Binary Quadratic forms
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Difference of a Hauptmodul for Γ_(0)(N ) and certain Gross-Zagier type CM value formulas 被引量:1
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作者 Dongxi Ye 《Science China Mathematics》 SCIE CSCD 2022年第2期221-258,共38页
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
关键词 Borcherds product the Gross-Zagier CM value formula monster denominator formula modular forms for the Weil representation
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An algorithm for computing the factor ring of an ideal in a Dedekind domain with finite rank
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作者 Dandan Huang Yingpu Deng 《Science China Mathematics》 SCIE CSCD 2018年第5期783-796,共14页
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
关键词 deterministic polynomial-time test Dedekind domains basis representation Hermite and Smith normal forms
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