p-adic polylogarithms and irrationality
نویسندگان
چکیده
منابع مشابه
FINITE AND p-ADIC POLYLOGARITHMS
The finite logarithm was introduced by Kontsevich (under the name “The 1 1 2 logarithm”) in [Kon]. The finite logarithm is the case n = 1 of the n-th polylogarithm lin ∈ Z/p[z] defined by lin(z) = ∑p−1 k=1 z /k. In loc. cit. Kontsevich proved that the finite logarithm satisfies a 4-term functional equation, known as the fundamental equation of information theory. The same functional equation is...
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In [BD92] (see also [HW98]), A. A. Beilinson and P. Deligne constructed the motivic polylogarithmic sheaf on PQ\{0, 1,∞}. Its specializations at primitive d-th roots of unity give the Beilinson’s elements of H M(Q(μd),Q(m)) = K2m−1(Q(μd))⊗ Q (m ≥ 1), whose images under the regulator maps to Deligne cohomology are the values of m-th polylogarithmic functions at primitive d-th roots of unity. The...
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Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa139-1-4