Titlebook: Computational Algebra and Number Theory; Wieb Bosma,Alf Poorten Book 1995 Springer Science+Business Media Dordrecht 1995 Category theory.G

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BROTH

Does the Set of Points of an Elliptic Curve Determine the Group?,natural way, the point at infinity being the zero element. It is often heard that the group structure on .(.) is “determined” by the fact that three points of .(.) add up to zero if they lie on a line. In this paper we investigate whether this statement is correct if taken literally. We find that it

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Bounds for Class Numbers of Quadratic Orders,+ . : ., . ∈ .}, and a . in .. is one which can be written as [., . + ..] where . = .(.) is the . of . and .. = .. + . for integers . and . with .. Here .. is the ., i.e. the square-free kernel of Δ, and we have that . = 2 if .. ≡ 1 mod 4 or . = 1 otherwise.

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Short Representation of Quadratic Integers, in log log H(.), log N(.) and log Δ where H(.) is the height of . and N(.) is the norm of .. We show that using compact representations we can in polynomial time compute norms, signs, products, and inverses of numbers in . and principal ideals generated by numbers in .. We also show how to compare

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Computing Aurifeuillian Factors,(.) and ..(.) are monic polynomials with integer coefficients. These coefficients can be computed by simple algorithms which require .(..) arithmetic operations over the integers. Also, there are explicit formulas and generating functions for ..(.) and ..(.). This paper is a preliminary report which

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Computation of Cyclotomic Polynomials with Magma,o illustrate many of the tools and features available in Magma for elementary number theory, on the other hand it provides an opportunity to present the results of some computations extending previously published tables about the first occurrence of integers as coefficients of cyclotomic polynomials

IVORY

On Some Characteristics of Uniformity of Distribution and Their Applications,veral classical measures such as discrepancy and exponential sums. They are connected to several problems from quite different areas such as choosing parameters of linear iteration processes for solving system of linear equations, choosing knots for polynomial interpolation, estimating the size of V

Cytology

Tartar

A New Generalisation of the Kummer Congruence,li number of Leopoldt and (.) is the binomial coefficient operator. This congruence is best possible in the sense that there does not exist a pair (.), where .. (≠1) is even, such that ..(.., .) ∈ ... for all . ≥ 0..The classical generalisation of the Kummer congruence is . It will be shown that thi

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