eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
4:1
4:3
10.4230/LIPIcs.FSTTCS.2020.4
article
Holonomic Techniques, Periods, and Decision Problems (Invited Talk)
Ouaknine, Joël
1
2
https://orcid.org/0000-0003-0031-9356
Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
Department of Computer Science, Oxford University, UK
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. In this talk, I will give an overview of the area, and in particular will present a select survey of known and original results on decision problems for holonomic sequences and functions. (Holonomic sequences satisfy linear recurrence relations with polynomial coefficients, and holonomic functions satisfy linear differential equations with polynomial coefficients.) I will 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 will 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol182-fsttcs2020/LIPIcs.FSTTCS.2020.4/LIPIcs.FSTTCS.2020.4.pdf
holonomic techniques
decision problems
recurrence sequences
minimal solutions
Positivity Problem
continued fractions
special functions
periods
exponential periods