学术活动

Modular Functions and Holonomic Functions

2019-10-25 16:00

报告人: Peter Paule

报告人单位: Johannes Kepler University of Linz

时间: 2019-10-25 16:00-17:00

地点: 卫津路校区6号楼108教

开始时间: 16:00

报告人简介: 教授

年: 2019

日月: 10.25

Holonomic (also called: D-finite) functions satisfy linear differential equations with polynomial coefficients-in contrast to modular functions.

Holonomic functions and the coefficient sequences of their Taylor series are ubiquitous objects in enumerative combinatorics. The coefficients of the Fourier expansions of modular functions often carry interesting number theoretic information. For example, the sequence p(4)=5, p(9)=30, p(14)=135, etc. are partition numbers which, as observed first by Ramanujan, are all divisible by 5.

The talk investigates various connections between holonomic and modular functions. To this end, computer algebra is used.


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