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The complete principal divisor lattices

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Science China Mathematics 2010年第8期53卷 2159-2172页

作者： WANG XuePing & QU XiaoBing College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China College of Mathematics and Software Science Sichuan Normal University Chengdu China

In this paper,we introduce a concept of principal divisor lattice and describe the structure of its *** first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible *** the end,we show the descriptions of lattices that have unique(***) irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.

关键词： complete lattice principal divisor lattice distributive lattice irredundant join irreducible decomposition

The divisor problem for arithmetic progressions

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Chinese Science Bulletin 1995年第4期40卷 265-267页

作者：李红泽 Department of Mathematics Shandong University Jinan 250100 China

Let n≥1 and r≥2 be integers and let dr（n） denote the number of ordered r-tuples （n1,…,nr） of natural numbers for which multiply from 1≤j≤r （nj）=n For （a,q）=1,define Dr（X,q,a）=sum from n≤X n≡a（modg） ... 详细信息

关键词： arithmetic progression divisor problem.

ON THE divisor PROBLEM

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Chinese Science Bulletin 1988年第17期33卷 1484-1485页

作者：张文鹏 Department of Mathematics Shandong University Jinan

For x>1, let, where the k-th divisor function dk（n） is defined by the series, so that d2（n）=d（n） is the

关键词： familiar divisor Heath inequality fourth

THE STRUCTURE OF ORTHOGONAL GROUPS OVER ARBITRARY COMMUTATIVE RINGS

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Chinese Annals of Mathematics,Series B 1989年第3期10卷 341-350页

作者：李福安 Institute of Mathematics Academia Sinica Beijing China

Let R be an arbitrary commutative ring, and n an integer≥3. It is proved for any ideal J of R thatEO2n（R, J）=[EO2n（R）, EO2n（J）]=[EO2n（R）, EO2n（R, J）]=[EO2n（R）, O2n（R,J）]=[O2n（R）, EO2n（R,J）].In particular, EO2n（R, J） is a normal subgroupof O2n（R）. Furthermore, the problem of normal subgroups of O2n（R） has an affirmative solution if and only if aR∩ Ann（2）=α2 Ann（2） for each a in R. In particular, if 2 is not a zero divisor in R, then the problem of normal subgroups of O2n（R） has an affirmative

关键词： subgroups commutative divisor integer OVER arbitrary rings nonzero lemma diagonal

On a conjecture of Chowla and Walum

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Science China Mathematics 2010年第10期53卷 2755-2771页

作者： TANIGAWA Yoshio Graduate School of of Mathematics Nagoya University

We show the asymptotic behaviour of the mean square of the sum n c√x naPk(x/n),where Pk(x) = Bk({x}) and Bk(x) denotes the Bernoulli polynomial of degree k and c > 0 is a real number such that c2 is *** result implie... 详细信息

关键词： the Dirichlet divisor problem error term mean square the Bernoulli polynomial the Vorono formula Chowla and Walum’s conjecture.

ON QUINTIC K-3 SURFACES

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Chinese Annals of Mathematics,Series B 1991年第2期12卷 181-191页

作者：杨劲根 Institute of Mathematics Fudan UniversityShanghaiChina.

If a non-normal quintic surface is birational to a K3 surface,then there are threepossibilities:either it is singular along a conic;or it is singular along two mutuallyintersecting lines;or it is singular along a line and has an isolated triple point outside *** if a K3 surface contains a hyperelliptic curve of genus three with anode or simple cusp,then it is birational to a quintic surface of the first type *** the other two cases,the minimal models are also characterized.

关键词： singular anode conic outside triple divisor assume desired union resolve

A note on a result of Abercrombie

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Chinese Science Bulletin 1997年第14期42卷 1151-1154页

作者： ZHAI WenguangDepartment of Mathematics, Shandong Normal University, Jinan 250014, China Department of Mathematics Shandong Normal University Jinan China

SUPPOSE θ∈[1,+ ∞) is any real number. The sequence B_θ={[nθ]|n∈N}is calledBeatty’s sequence determined by θ. Beatty sequences have been the subject of intensive inves-tigation in recent years on account of the... 详细信息

关键词： Bealty’s sequence divisor problem rational approximation.

BERNOULLI-GOSS POLYNOMIAL AND CLASS NUMBER OF CYCLOTOMIC FUNCTION FIELDS

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Science China Mathematics 1990年第6期33卷 654-662页

作者：冯克勤高文云 Department of Mathematics University of Science and Technology of China Hefei 230026 PRC

Let k = Fq(T),q=pn, and let K=k((?)p)be the cyclotomic function field with conduc-tor P = P(T), and suppose K+ is the maximal real subfield of K, hp(h+p) is the class number of divisor group (of degree zero) of K(K+), and h-p=hp/h+p(∈ Ⅱ). This paper proves that for any fixed q≥3, there exist infinite many irreducible manic polynomial P∈Fq[T] such that p\h+p and pq-2\h-p. In addition, all regular quadratic irreducible polynomials in Fq[T] for 2≤p≤269 are determined.

关键词： cyclotomic function field class namber of divisor group Bernoulli-Goss polynomial

On the Distribution of {x/n}

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Chinese Science Bulletin 1993年第19期38卷 1596-1600页

作者：王炜 Institute of Mathematics Shanodong University Jinan 250100 PRC

1 Introduction Let x be a large real number. Study of the famous Dirichlet’s divisor problem suggests that for positive integers n≤x. Distribution of {x/n} in [0, 1) is fairly even. For any given real number α sati... 详细信息

关键词： divisor problem exponent pairs trigonometric sums.