Hamza Yesilyurt

Affiliation: Bilkent University, Ankara

Email: hamza@fen.bilkent.edu.tr

Title Of Talk: On Rogers--Ramanujan functions, binary quadratic forms and eta-quotients

Abstract: In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers--Ramanujan functions. We observe that the function that appears in Ramanujan's identities can be obtained from a Hecke action on a certain family of eta products. We establish further Hecke-type relations for these functions involving binary quadratic forms. Our observations enable us to find new identities for the Rogers--Ramanujan functions and also to use such identities in return to find identities involving binary quadratic forms such as
((4,1,22)-(10,7,10))/((1,1,88)-(9,3,10)) =((5,3,18)-(8,1,11))((2,1,44)-(8,1,11)) =q^3E(q^3)E(q^117)/E(q^9)/E(q^39).
This is a joint work with Alexander Berkovich.

Last update made Mon Oct 8 19:51:03 EDT 2012.
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