Periods and elementary real numbers Export

@article{citeulike:5778246, abstract = {The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced from computational complexities. In particular we prove that periods can be effectively approximated by elementary rational Cauchy sequences. As an application, we exhibit a computable real number which is not a period.}, archivePrefix = {arXiv}, author = {Yoshinaga, Masahiko}, citeulike-article-id = {5778246}, citeulike-linkout-0 = {http://arxiv.org/abs/0805.0349}, citeulike-linkout-1 = {http://arxiv.org/pdf/0805.0349}, day = {3}, eprint = {0805.0349}, keywords = {algebraic\_geometry, algebraic\_number\_theory, periods}, month = {May}, posted-at = {2009-09-12 15:11:07}, priority = {2}, title = {Periods and elementary real numbers}, url = {http://arxiv.org/abs/0805.0349}, year = {2008} }

TY - JOUR ID - citeulike:5778246 L3 - citeulike-article-id:5778246 N2 - The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced from computational complexities. In particular we prove that periods can be effectively approximated by elementary rational Cauchy sequences. As an application, we exhibit a computable real number which is not a period. TI - Periods and elementary real numbers KW - algebraic_geometry KW - algebraic_number_theory KW - periods AU - Yoshinaga, Masahiko PY - 2008/May/03/ UR - http://arxiv.org/abs/0805.0349 ER -