| Full text | |
| Author(s): |
Viu-Sos, Juan
[1]
Total Authors: 1
|
| Affiliation: | [1] Inst Matematica Pura & Aplicada, Est. Dona Castorina, 110, Jardim Bot, BR-22460320 Rio De Janeiro, RJ - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF NUMBER THEORY; v. 17, n. 01, p. 147-174, FEB 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
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 Ralg-semi-algebraic set obtained from any integral representation by an effective algorithm satisfying the rules allowed by the Kontsevich-Zagier period conjecture. (AU) | |
| FAPESP's process: | 16/14580-7 - Applications of singularity theory: differential geometry and algebraic geometry |
| Grantee: | Juan Viu Sos |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |