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Abstracts for Discoverers avant le PhD (DISCO)

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Radial Limits of a universal mock theta function

Posted in
Speaker: 
Min-Joo Jang and Steffen Loebrich
Affiliation: 
(both U Cologne)
Date: 
Wed, 02/09/2015 - 14:15 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Discoverers avant le PhD (DISCO)

In his last letter to Hardy, Ramanujan provided 17 examples
for what he called a "mock theta function". These are given by
q-hypergeometric series that have the same growth behavior as classical
modular forms as one radially approaches roots of unity from within the
unit disc.
             We find explicit formulas for radial limits of a universal
mock theta function, which can express every mock theta function.

Convergence Properties of the Classical and Generalized Rogers-Ramanujan Continued Fractions

Posted in
Speaker: 
Alexandru Ciolan
Affiliation: 
U Bonn
Date: 
Wed, 02/09/2015 - 15:10 - 15:55
Location: 
MPIM Lecture Hall
Parent event: 
Discoverers avant le PhD (DISCO)

The aim of this talk is to present some new results about the convergence and divergence of the classical and generalized Rogers-Ramanujan continued fractions on the unit circle, obtained during the Cologne Young Researchers in Number Theory Program 2015. We provide an example of an uncountable set of measure zero on which the Rogers-Ramanujan continued fraction R(x) diverges and which enlarges a set previously found by Bowman and Mc Laughlin.

Problem potpourri session

Posted in
Affiliation: 
U Bonn
Date: 
Wed, 02/09/2015 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
Discoverers avant le PhD (DISCO)

 

Here anybody can present some open problems where
likely with limited mathematical machinary something can
be achieved (so that really junior mathematicians have a
chance to resolve this).
 Likewise, also junior mathematicians can present problems.

 

 

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