Some new identities from the Ramanujan-Kolberg algorithm

Beschreibung

Ramanujan’s identities involving the generating functions forp(5n+ 4) and p(7n+ 5) are considered to be among his finest results. These were shown by Kolberg to be special cases of a larger class of relationships expressing generating functions for p(mn+j) in terms of eta quotients. The form of these identities is prevalent throughout the theory of partitions. They are useful in the verification of families of partition congruences, as well as in the study of certain conjectures in the theory of modular functions. In 2014 Silviu Radu developed an algorithm to compute the Ramanujan-Kolberg identities inherent in various arithmetic functions. This algorithm has now been given a complete implementation. We will show some interesting examples found using the algorithm. We include some new results, as well as some interesting improvements on established partition congruences.

Zeitraum	07 Juni 2019
Ereignistitel	Analytic and Combinatorical Number Theory: The Legacy of Ramanujan - in honor of Prof. Bruce Berndt's 80th birthday
Veranstaltungstyp	Konferenz
Ort	USA/Vereinigte StaatenAuf Karte anzeigen