14,431 research outputs found
TORSION POINTS WITH MULTIPLICATIVELY DEPENDENT COORDINATES ON ELLIPTIC CURVES
No full textIn this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication
ON THE CARMICHAEL RINGS, CARMICHAEL IDEALS AND CARMICHAEL POLYNOMIALS
No full textMotivated by Carmichael numbers, we say that a finite ring R is a Carmichael ring if a(vertical bar R vertical bar) = a for any a is an element of R. We then call an ideal I of a ring R a Carmichael ideal if R/I is a Carmichael ring, and a Carmichael element of R means it generates a Carmichael ideal. In this paper, we determine the structure of Carmichael rings and prove a generalization of Korselt's criterion for Carmichael ideals in Dedekind domains. We extend several results from the number field case to the function field case. In particular, we study Carmichael elements of polynomial rings over finite fields (called Carmichael polynomials) by generalizing some classical results. For example, we show that there are infinitely many Carmichael polynomials but they have zero density.
On the Lucas and Lehmer sequences in Dedekind domain
No full textIn this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences
in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the primitive divisor results for such sequences in function fields
On abelian multiplicatively dependent points on a curve in a torus
No full textWe show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite set of primitive characters from Gmn to Gm restricted to the curve, and a finite set. We also introduce the notion of primitive multiplicative dependence and obtain a finiteness result for primitively multiplicatively dependent points defined over a so-called Bogomolov extension of a number field
On multiplicatively dependent vectors of algebraic numbers
No full textIn this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of xed degree, or within a xed number eld, and bounded height
Author Correction: Human fingerprint in global weather
No full textIn the version of this News & Views originally published, the ref. 5 author surnames Meihnausen, Fisher and Szekely were spelled incorrectly; they should have been spelled Meinshausen, Fischer and Székely, respectively. This has now been corrected. © 2020, Springer Nature Limited.11Nsciessciscopu
<Note>So－called "The Commencement Essays of Chai－min－sha－shu 斉民要術"
No full text斉民要術の巻頭雑説は、要術の著者賈思勰の筆ではなく、要術にない蕎麦や糙種などの語が見られるため、後人の作が添加されたものと一般に考えられている。それに対し私は本論において、要術中の瞿麦は蕎麦と思われるし、しかも技術的にみて、要術の整地法は、現在と同じく耕－耙－労の三段階なのに対し、雑説は耕－労の二段階になっているので、雑説は要術より古いものと考えるのが常識的であり、蕎麦や糙種など新らしいと思われる語の混入しているのは、転写中にその時の慣用語に改ためられたものではないかとの見解を提出するものである。The Commencement essays of "Chai-min-sha-shu" 斉民要術 were not by "Ku-szu-hsieh" 賈思勰, writor of the book, but were thought to be the addition by posterity, judging from the terms of "Chiao-mai" 蕎麦 and "Ts'ao-chung" 糙種 which were not found in "Sha-shu" 要術. In this article, "Ch'ü-mê" 瞿麦 in "Sha-shu" 要術 is considered as "Chiao-mai" 蕎麦, and from the technical point of view the way of cultivation in "Sha-shu", like that of the present time, consisted in the three-stage system, "Kêng-pa-lao" 耕--耙--労, thought in the commencement essays in the two-stage system, "Kêng--lao" 耕--労; therefore, it is sensible that the commencement essays were, to be thought, older than "Sha-shu" 要術 and mixture of the new terms like "Chao-mai" and "Ts'ao-chung" 糙種 may be from revision of the terms to the then idioms in transcription
Towards a national puppet centre for the Lebanon
No full textThe impression that Arabs did not attempt to express themselves through the medium of dramatic arts till recently echoes a simultaneous conviction which
prevailed concerning visual arts expression. Early in the second half of this century, researchers started questioning whether Arabs could have expressed
themselves in visual or dramatic representations under the auspices of Islam. Meanwhile, we have been rediscovering our visual, oral and dramatic art heritage through a Western cultural perspective.
The aim of this research is to examine the sources of inspiration which have been shaping the visual and dramatic art traditions in the Arab Middle East region over the past five thousand years. Little attention has been given to the
interplay between the various forms of artistic expression in the Middle East. Besides, much less concern has been articulated about the performance arts interpretation of the notion of abstraction which characterises the artistic
expressions of the region.
One performance art form that has gone a long way in the direction towards abstraction is puppetry. From the times of the Pharaohs and Mesopotamians, puppets and masked actors communicated myths and legends in religious rituals
and festivals. Later, puppets continued under Islam to communicate secular themes and narratives.
Puppets, by their nature, involve the concept of alienation and enable the modern Arab to present ideas in a manner consistent with his intellectual, cultural and aesthetic predilections.
In its search for forms of dramatic expression the Lebanese theatre might profitably look into its own cultural heritage, try to learn from and experiment with the various types of oral and performance traditions especially puppetry which has been long forgotten
Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes
No full textFor positive integers K and L, we introduce and study the notion of K-multiplicative dependence over the algebraic closure of a finite prime field Fp, as well as L-linear dependence of points on elliptic curves in reduction modulo primes. One of our main results shows that, given non-zero rational functions φ1,...,φm,ρ1,...,ρn ∈ Q(X) and an elliptic curve E defined over the integers Z, for any sufficiently large prime p, for all but finitely many α in the algebraic closure of F_p, at most one of the following two can happen: φ1(α),...,φm(α) are K-multiplicatively dependent or the points (ρ1(α),⋅),...,(ρn(α),⋅) are L-linearly dependent on the reduction of E modulo p. As one of our main tools, we prove a general statement about the intersection of an irreducible curve in the split semiabelian variety G^k_m×E^n with the algebraic subgroups of codimension at least 2.
As an application of our results, we improve a result of M. C. Chang and extend a result of J. F. Voloch about elements of large order in finite fields in some special cases
- …
