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Some q-series expansions related to Ramanujan's theta functions

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时间:2019-11-25  来源:

题目:         Some q-series expansions related to Ramanujan's theta functions

报告人:    唐大钊 (天津大学应用数学中心)

时间地点: 2019.11.26  09:00am  N219

摘要:       The study on vanishing coefficients in infinite product expansions, which was derived from the Hardy-Ramanujan-Rademacher expansions for quotients of certain infinite products, could be traced back to Richmond and Szekeres. Later, Andrews and Bressoud, Alladi and Gordon, as well as Mc Laughlin proved some generalizations of Richmond and Szekeres's result. Motivated by the recent work of Hirschhorn on vanishing coefficients of the arithmetic progressions in two q-series expansions, in this talk, we study some variants and prove some comparable results. Moreover, we also investigate vanishing coefficients of the arithmetic progressions in four quotients of infinite product expansions and obtain some analogous results. Finally, we also give some recent progress and two sign conjectures of coefficients in several types of q-series expansions.
This is a joint work with Ernest X. W. Xia.

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