Title: | Combinatorial and asymptotic properties of Ramanujan's function \sum_{n=0}^{\infty} \frac{q^{n^{2}} z^{n} }{(q;q)_{n}}. |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Tim Huber, Iowa State University |

Abstract: |

The Hadamard product for a generalization of the Rogers-Ramanujan series appears on page 57 of Ramanujan's Lost Notebook. Coefficients appearing in series expansions for zeros of Ramanujan's function have interesting analytic and combinatorial properties. This lecture will explore connections between the zeros of Ramanujan's function and classical objects such as the Jacobian
elliptic functions, q-analogues of the trigonometric and gamma functions, orthogonal polynomials, and the Lambert W function. The discussion will include recent joint work with Ae Ja Yee on the arithmetic interpretation of new q-analogues of the tangent numbers arising in expressions for the zeros of Ramanujan's function. |