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A semi-canonical reduction for periods o...
Viu-Sos, Juan...

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A semi-canonical reduction for periods of Kontsevich-Zagier by Viu-Sos, Juan ( Author )
Lemonjar Open Access
N.A
03-09-2015
The Q¯¯¯¯-algebra of periods was introduced by Kontsevich and Zagier as complex numbers whose real and imaginary parts are values of absolutely convergent integrals of Q-rational functions over Q-semi-algebraic domains in Rd. The Kontsevich-Zagier period conjecture affirms that any two different integral expressions of a given period are related by a finite sequence of transformations only using three rules respecting the rationality of the functions and domains: additions of integrals by integrands or domains, change of variables and Stokes formula. In this paper, we prove that every non-zero real period can be represented as the volume of a compact Q¯¯¯¯∩R-semi-algebraic set, obtained from any integral representation by an effective algorithm satisfying the rules allowed by the Kontsevich-Zagier period conjecture.
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English
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http://arxiv.org/abs/1509.01097
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