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标题：Holonomic Techniques, Periods, and Decision Problems (Invited Talk)
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作者：Ouaknine, Joël
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：202
DOI：10.4230/LIPIcs.MFCS.2021.3
语种：English
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Holonomic techniques have deep roots going back to Wallis, Euler, and Gauss, and have evolved in modern times as an important subfield of computer algebra, thanks in large part to the work of Zeilberger and others over the past three decades (see, e.g., [Doron Zeilberger, 1990; Petkovšek et al., 1997]). In this talk, I give an overview of the area, and in particular present a select survey of known and original results on decision problems for holonomic sequences and functions. I also discuss some surprising connections to the theory of periods and exponential periods, which are classical objects of study in algebraic geometry and number theory; in particular, I relate the decidability of certain decision problems for holonomic sequences to deep conjectures about periods and exponential periods, notably those due to Kontsevich and Zagier.Parts of this exposition draws upon [George Kenison et al., 2021].
关键词：Holonomic and hypergeometric sequences;Inequality problems;Continued fractions;Periods