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New fifth and seventh order mock theta function identitiesJul 10 2019We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients ... More

K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite ProductsFeb 01 2007We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function ... More