Holonomic Functions and Modular Forms: An Algorithmic Bridge
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA)
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
Holonomic functions and sequences satisfy linear differential and dif- ference equations, respectively, with polynomial coeffcients. It has been estimated that holonomic functions cover about 60 percent of the functions contained in the 1964 "Handbook" by Abramowitz and Ste- gun. A recent estimate says that holonomic sequences constitute about 20 percent of Sloane's OEIS database. The study of these ubiquitous objects traces back to the time of Gauss (at least). Also tracing back to the time of Gauss (at least) are highly non-holonomic objects: modular functions and modular forms with q-series representations arising, for instance, as generating func- tions of partitions of various kinds. Using computer algebra, the talk connects these two different worlds. Applications concern partition congruences, Fricke-Klein relations, ir- rationality proofs a la Beukers, or approximations to pi studied by Ramanujan and the Borweins. As a major ingredient to a "first guess, then prove" strategy, a new algorithm for proving differential equations for modular forms is used. The results presented arose in joint work with Silviu Radu (RISC).
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Vortragsdatum:
14.06.2022
Vortragsort:
Virtuell
Details zum Vortragsort:
online aufgrund von Planungsunsicherheiten wegen der Corona Pandemie
Forschungs-