منابع مشابه
Finite Field Arithmetic
11.1 Prime fields of odd characteristic 201 Representations and reductions • Multiplication • Inversion and division • Exponentiation • Squares and square roots 11.2 Finite fields of characteristic 2 213 Representation • Multiplication • Squaring • Inversion and division • Exponentiation • Square roots and quadratic equations 11.3 Optimal extension fields 229 Introduction • Multiplication • Exp...
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For integers, the parameter n is the bit-length, and for the finite field Fq we let n = log q. In the case of polynomial root-finding, d is the degree of the polynomial and we list bounds on the expected running time since these operations are most efficiently implemented using probabilistic algorithms. In Lecture 3 we addressed the cost of addition and subtraction in both Z and Fq, and the cos...
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This is a brief report on recent work of the author (some joint with Greg Anderson) and his student on multizeta values for function fields. This includes definitions, proofs and conjectures on the relations, period interpretation in terms of mixed CarlitzTate t-motives and related motivic aspects. We also verify Taelman’s recent conjectures in special cases. 2010 Mathematics Subject Classifica...
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Z = {integers} Q = {rational numbers} R = {real numbers} C = {complex numbers} Z+ = { positive integers} q = a power of a prime p Fq = A Finite field with q elements A = Fq[t] A+ = {monics in A} K = Fq(t) K∞ = Fq((1/t)) = completion of K at ∞ C∞ = completion of algebraic closure of K∞ [n] = tq n − t dn = ∏n−1 i=0 (t qn − tqi) `n = ∏n i=1(t− tq i ) deg = function assigning to a ∈ A its degree in...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1988
ISSN: 0001-8708
DOI: 10.1016/0001-8708(88)90082-5