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检索条件"主题词=algorithmic number theory"
12 条 记 录,以下是1-10 订阅
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Seventeen lines and one-hundred-and-one points
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THEORETICAL COMPUTER SCIENCE 2004年 第2-3期321卷 415-421页
作者: Woeginger, GJ Univ Twente Dept Math NL-7500 AE Enschede Netherlands
We investigate a curious problem from additive number theory: Given two positive integers S and Q, does there exist a sequence of positive integers that add up to S and whose squares add up to Q? We show that this pro... 详细信息
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
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SIAM REVIEW 1999年 第2期41卷 303-332页
作者: Shor, PW AT&T Bell Labs Res Florham Pk NJ 07932 USA
A digital computer is generally believed to be an efficient universal computing device;that is, it is believed to be able to simulate any physical computing device with an increase in computation time by at most a pol... 详细信息
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Abelian lifts of polynomials
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JOURNAL OF number theory 2023年 246卷 265-278页
作者: Wong, Siman Univ Massachusetts Dept Math & Stat Amherst MA 01003 USA
Let p be a prime, and let f is an element of Z[x] be a non-constant polynomial whose leading coefficient is prime to p and that f has no repeated root modulo p. Suppose the mod -p irreducible factors off all have the ... 详细信息
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How to compute the coefficients of the elliptic modular function j(z)
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EXPERIMENTAL MATHEMATICS 2003年 第1期12卷 115-121页
作者: Baier, H Köhler, G TH Darmstadt Darmstadt Ctr IT Secur D-64283 Darmstadt Germany Univ Wurzburg Dept Math D-97074 Wurzburg Germany
We discuss various methods to compute the Fourier coefficients of the elliptic modular function j(z). We present run times to compute the coefficients in practice. If possible, we discuss the theoretical complexity of... 详细信息
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Computing generators of the tame kernel of a global function field
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JOURNAL OF SYMBOLIC COMPUTATION 2006年 第9期41卷 964-979页
作者: Weng, Annegret Univ Mainz Fachbereich Math D-55128 Mainz Germany
The group K-2 of a curve C over a finite field is equal to the tame kernel of the corresponding function field. We describe two algorithms for computing generators of the tame kernel of a global function field. The fi... 详细信息
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Approximating the number of integers free of large prime factors
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MATHEMATICS OF COMPUTATION 1997年 第220期66卷 1729-1741页
作者: Hunter, S Sorenson, J Department of Mathematics and Computer Science Butler University
Define psi(x, y) to be the number of positive integers n less than or equal to x such that n has no prime divisor larger than y. We present a simple algorithm that approximates psi(x,y) in O(y{log log x/log y + 1/log ... 详细信息
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Computation of Euclidean minima in totally definite quaternion fields
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INTERNATIONAL JOURNAL OF number theory 2019年 第1期15卷 43-66页
作者: Cerri, Jean-Paul Lezowski, Pierre Univ Bordeaux IMB 351 Cours Liberat F-33400 Talence France Univ Clermont Auvergne Lab Math Blaise Pascal F-63000 Clermont Ferrand France
We describe an algorithm that allows to compute the Euclidean minimum (for the norm form) of any order of a totally definite quaternion field over a number field K of degree strictly greater than 1. Our approach is a ... 详细信息
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ON THE MINIMAL number OF SMALL ELEMENTS GENERATING FINITE PRIME FIELDS
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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2017年 第2期96卷 177-184页
作者: Munsch, Marc 5010 Inst Anal & Zahlentheorie Steyrergasse 30 A-8010 Graz Austria
In this note, we give an upper bound for the number of elements from the interval [1, p(1/4 root e+is an element of)]necessary to generate the finite field F-p(*) with p an odd prime. The general result depends on the... 详细信息
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Collatz Conjecture for 2100000-1 is True - Algorithms for Verifying Extremely Large numbers  4
Collatz Conjecture for 2<SUP>100000</SUP>-1 is True - Algori...
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IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI)
作者: Ren, Wei Li, Simin Xiao, Ruiyang Bi, Wei China Univ Geosci Hubei Key Lab Intelligent Geoinformat Proc Sch Comp Sci Wuhan 430074 Peoples R China Guizhou Univ Guizhou Prov Key Lab Publ Big Data Guizhou Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China China Univ Geosci Sch Comp Sci Sch Math & Phys Wuhan 430074 Peoples R China SeeleTech Corp San Francisco CA 94107 USA
Collatz conjecture (or 3x+1 problem) has been explored for about 80 years. By now the largest number that has been verified for Collatz conjecture is about 60 bits. In this paper, we propose new algorithms that can ve... 详细信息
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Primality proving using elliptic curves with complex multiplication by imaginary quadratic fields of class number three
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FINITE FIELDS AND THEIR APPLICATIONS 2024年 99卷
作者: Onuki, Hiroshi Univ Tokyo Dept Math Informat 7-3-1 HongoBunkyo Ku Tokyo 1138656 Japan
In 2015, Abatzoglou, Silverberg, Sutherland, and Wong presented a framework for primality proving algorithms for special sequences of integers using an elliptic curve with complex multiplication. They applied their fr... 详细信息
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