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hecke OPERATOR AND PELLIAN EQUATION CONJECTURE Ⅲ

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Systems Science and Mathematical Sciences 1991年第2期4卷 97-103页

作者：陆洪文 Department of Mathematics University of Science and Technology of ChinaHefei 230026China

In this note,we give a relationship between the Mordell conjecture on the Pellianequation and the action of the hecke operator on the Hirzebruch sum.

关键词： hecke operator Pellian equation continued fractions zeta function

On Subsets of Q(√m) Q under the Action of hecke Groups H(λq)

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Applied Mathematics 2014年第8期5卷 1284-1291页

作者： M. Aslam Malik M. Asim Zafar Center for Undergraduate Studies University of the Punjab Quaid-e-Azam Campus Lahore Pakistan Department of Mathematics University of the Punjab Quaid-e-Azam Campus Lahore Pakistan

is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two hecke groups—the full modular group and the group of linear-fractional transformations on . In particular, we investigate the action of on for finding different orbits.

关键词： Quadratic Irrationals hecke Groups Legendre Symbol G-Set

On the least primitive root in number fields

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Science China Mathematics 2010年第9期53卷 2489-2500页

作者： WANG TianZe1,& GONG Ke21School of Mathematics and Information Sciences,North China University of Water Resources and Electric Power,Zhengzhou 450011,China 2Department of Mathematics,Henan University,Kaifeng 475004,China 1. School of Mathematics and Information Sciences North China University of Water Resources and Electric Power Zhengzhou 450011 China2. Department of Mathematics Henan University Kaifeng 475004 China

Let K be an algebraic number field and OK its ring of *** any prime ideal p,the group(OK/p) of the reduced residue classes of integers is *** call any element of a generator of the group(OK/p) a primitive root modulo *** both by Shoup's bound for the rational improvement and Wang and Bauer's generalization of the conditional result of Wang Yuan in 1959,we give in this paper a new bound for the least primitive root modulo a prime ideal p under the Grand Riemann Hypothesis for algebraic number *** results can be viewed as either the improvement of the result of Wang and Bauer or the generalization of the result of Shoup.

关键词： primitive root algebraic number fields hecke zeta function

Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory

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Advances in Pure Mathematics 2013年第2期3卷 246-253页

作者： Francisco Bulnes Department of Research in Mathematics and Engineering Tecnológico de Estudios Superiores de Chalco Chalco Mexico

We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding hecke category.

关键词： Penrose Transform Coherent G-Quasi-Equivariant D-Modules hecke Sheaf Moduli Stacks Moduli Spaces

Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms

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Advances in Pure Mathematics 2014年第6期4卷 253-260页

作者： Francisco Bulnes Research Department in Mathematics and Engineering Tecnológico de Estudios Superiores de Chalco Chalco Mexico

Some derived categories and their deformed versions are used to develop a theory of the ramifications of field studied in the geometrical Langlands program to obtain the correspondences between moduli stacks and solution classes represented cohomologically under the study of the kernels of the differential operators studied in their classification of the corresponding field equations. The corresponding D-modules in this case may be viewed as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform) naturally arising in the framework of conformal field theory. Inside the geometrical Langlands correspondence and in their cohomological context of strings can be established a framework of the space-time through the different versions of the Penrose transforms and their relation between them by intertwining operators (integral transforms that are isomorphisms between cohomological spaces of orbital spaces of the space-time), obtaining the functors that give equivalences of their corresponding categories.(For more information,please refer to the PDF version.)

关键词： Geometrical Langlands Correspondence hecke Categories Moduli Stacks Penrose Transforms Quasi-Coherent Sheaves

椭圆曲线L(1)的3-adic赋值达到下界的判别

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华东师范大学学报（自然科学版） 2007年第5期 12-19页

作者：孙乃喆天津科技大学数学系天津300457

设K为三次分圆域,E_(Dλ):y^2=x^3-2~43~3D~λ为定义在K上的椭圆曲线,其中D为K中无平方因子的代数整数,λ∈Z.邱德荣用一个非常复杂的函数给出了当λ=2.4时E_(Dλ)的hecke L-函数在点1处的值(除以椭圆周期)恰被3^((n/2)-1)整除的充要条... 详细信息

设K为三次分圆域,E_(Dλ):y^2=x^3-2~43~3D~λ为定义在K上的椭圆曲线,其中D为K中无平方因子的代数整数,λ∈Z.邱德荣用一个非常复杂的函数给出了当λ=2.4时E_(Dλ)的hecke L-函数在点1处的值(除以椭圆周期)恰被3^((n/2)-1)整除的充要条件.本文用加权图的语言给出了这个充要条件一个简单的组合论的刻画.

关键词：椭圆曲线复乘 hecke L-函数加权图生成树

关于椭圆曲线ED^2：y^2=x^3-D^2x的BSD猜想

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四川大学学报（自然科学版） 2013年第3期50卷 470-476页

作者：韩冬春四川大学数学学院成都610064

令D=pq,其中p,q≡3(mod8)是不同的素数.本文计算了椭圆曲线ED2:y2=x3-D2 x的hecke L-函数在s=1处之值除以椭圆曲线的实周期ω的2部分,恰好是4,且Tate-Shafarevich群的2部分是1.由Rubin关于有复乘的椭圆曲线的重要结果可知BSD猜想对本文... 详细信息

令D=pq,其中p,q≡3(mod8)是不同的素数.本文计算了椭圆曲线ED2:y2=x3-D2 x的hecke L-函数在s=1处之值除以椭圆曲线的实周期ω的2部分,恰好是4,且Tate-Shafarevich群的2部分是1.由Rubin关于有复乘的椭圆曲线的重要结果可知BSD猜想对本文中的椭圆曲线成立.

关键词：椭圆曲线 BSD猜想 hecke L-函数

Building and Groups Ⅰ

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Chinese Quarterly Journal of Mathematics 2020年第1期35卷 1-28页

作者： LAI King-fai LIANG Zhi-bin School of Mathematics and Statistics Henan UniversityKaifengHenan475004China School of Mathematical Sciences Capital Normal UniversityBeijing100048China

This is a pedagogical introduction to the theory of buildings of Jacques Tits and to some applications of this *** paper has 4 *** the first part we discuss incidence geometry,Coxeter systems and give two definitions of *** study in the second part the spherical and affine buildings of Chevalley *** the third part we deal with Bruhat-Tits theory of reductive groups over local *** we discuss the construction of the p-adic flag manifolds.

关键词： Buildings Incidence geometry Coxeter groups Chevalley groups Reductive groups hecke algebras P-adic symmetric spaces