Some new identities from the Ramanujan-Kolberg algorithm
Sprache des Vortragstitels:
Analytic and Combinatorical Number Theory: The Legacy of Ramanujan - in honor of Prof. Bruce Berndt's 80th birthday
Sprache des Tagungstitel:
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.
Sprache der Kurzfassung:
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