Elliptic Curves of Twin-Primes Over Gauss Field and Diophantine Equations

Letp,qbetwinprimenumberswithq-p=2.ConsidertheellipticcurvesE=EcisalsodenotedasE orE-wheng= 1or-l.HeretheMordell-WeilgroupandtherankoftheellipticcurveEovertheGaussfieldK=q(r1)(andovertherationalfieldQ)willbedeterminedinseveralcases;andresultsofsolutionsforrelatedDiophantineequationsandsimultaneousPellianequationswillbegiven.ThearithmeticconstructsoverQoftheellipticcurveEhavebeenstudiedin[ll,theSelmergroupsaredetermined,resultsonMordell-Weilgroup,rank,Shafarevich-Tategroup,andtorsionsubg…     

Mordell-Weil groups and Selmer groups of twin- prime elliptic curves

Let E = Eσ : y2 = x(x + σp)(x + σq) be elliptic curves, where σ = ±1, p and q are primenumbers with p+2 = q. (i) Selmer groups S(2)(E/Q), S(φ)(E/Q), and S(φ)(E/Q) are explicitly determined,e.g. S(2)(E+1/Q)= (Z/2Z)2, (Z/2Z)3, and (Z/2Z)4 when p ≡ 5, 1 (or 3), and 7(mod 8), respectively. (ii)When p ≡ 5 (3, 5 for σ = -1) (mod 8), it is proved that the Mordell-Weil group E(Q) ≌ Z/2Z Z/2Z,symbol, the torsion subgroup E(K)tors for any number field K, etc. are also obtained.     

一般四次循环域的十个Ankeny-Artin-Chowla型类数公式

设K为四次循环数域,k为其二次子域,记h(L)为域L的理想类数。本文得到h^-=h(K)/h(k)的十个同余公式。特别若,素数p=r²+s²,s为偶数,则当p≡1(8)时,C₁h^-≡B_(p-1)/4B_3(p-1)/4(mod ρ),B_n是Bernoulli数;当ρ≡5(8)时,C₂h^-≡E_(ρ-5)/8E_(3ρ-7)/8(mod ρ),E_n是Euler数。若实则。若3在K=Q(√θ)分歧,则C₄h^-≡h(K*)/h(k)(mod 3),K*=Q(√3θ).C_i均为明显给出常数.此外还得到h^-可能因子的一些关系。这些结果相当于系统地把Ankeny-Arun-Chowla,Kiselev,Carlitz,陆洪文等从1948到1983年关于二次域的许多结果推广到四次循环域上去。     

反馈重传差错控制系统中检错码性能的分析

在数字通信差错控制系统的设计和使用中,要求对检错码的性能作一定的、明确的分析比较。我们对常用的三个主要检错码的性能作了初步分析比较。 我们假定通信方式是连续半双工的,信道分为主信道和反馈信道,图一是简单的方框图。信源发出的信息经过编码后送入主信道传输,主信道输出的码组首先进入检错器,若检测不出错误就送入译码器,译出的信息送信宿。但若检错器检测出码组有错,就不把此码组送译码器,而且由反馈信道要求重发。发送器接收到要求重发信号时,在发完正在发     

四次循环域类数模2的幂的同余公式

设K=k（√θ）是实四次循环域,k是其二次子域,K^-=k（√-θ）是相应的虚四次循环域．把K,k和K^-的类数分别记为hK,hk和kK^-,本文通过研究p-adic L-函数,得到了相对类数h^-=hK／hk和h^--=hK^-／hk的模2的幂的同余公式．     

RESEARCH ANNOUNCEMENTS Continued Fractions of Functions Connec …

The theory of continued fractions is very useful in studying real quadratic number fields (see ［2-5］).E. Artin in ［1］ introduced continued fractions of functions to study quadratic function fields, using formal Laurent expansions, which isessentially the theory of completion of the function fields at the infinite valuation. Here we first re-developthe theory of continued fractions of functions in a more elementary and manipulable manner mainly using long division of polynomials; and then study properties of the continued fractions, which will have important applications in studying quadratic function fields obtaining remarkable results on unit groups, class groups, and class numbers.