Department of Mathematics and Computer Science  
Number Theory and Combinatorics Seminar  
Spring 2021  
Until further notice, all talks will be given online  
For more information,
contact Nathan Ng
<nathan.ng@uleth.ca>
or Dave Morris
<Dave.Morris@uleth.ca>.
Talks are usually at noon on Monday. All times are Mountain Time. 
The next talk:  


Jan 18
Thursday at noon online 
Micah Milinovich
(University of Mississippi) 
Irregularities of Dirichlet Lfunctions and a Chebyshevtype bias for zeros
We describe a thin family of Dirichlet Lfunctions which have an irregular and perhaps unexpected behavior in their value distribution. This behavior has an arithmetic explanation and corresponds to the nonvanishing of a certain Gauss type sum. We give a complete classification of the characters for which these sums are nonzero and count the number of corresponding characters. It turns out that this Gauss type sum vanishes for 100% of primitive Dirichlet characters but there is an infinite (but zero density) subfamily of characters where the sum is nonzero. Experimentally, this thin family of Lfunctions seems to have a significant and previously undetected bias in distribution of gaps between their zeros. After uncovering this bias, we reexamined the gaps between the zeros of the Riemann zetafunction and discovered an even more surprising phenomenon. If we list the gaps in increasing order and sum over arithmetic progressions of gaps, there seems to be a "Chebyshevtype" bias in the corresponding measures; the sum over certain arithmetic progressions of gaps are much larger than others! These observations seem to go well beyond the Random Matrix Theory model of Lfunctions. This is joint work with Jonathan Bober and Zhenchao Ge. 

Zoom link and password: available from the organizers (Nathan.Ng@uleth.ca or Dave.Morris@uleth.ca) If possible, please write from a verifiable university email address, and not at the last minute.  
Click on any title for more info, including the abstract. Then
click on it again to hide the info.
When available, click on the mathtube icon to access a videorecording of the talk. 
Date  Speaker  Title  


Jan 18  everyone  Organizational meeting and problem session  


Jan 28  Micah Milinovich  Irregularities of Dirichlet Lfunctions and a Chebyshevtype bias for zeros  
Thursday 
(University of Mississippi)  


Feb 1  Quanli Shen  Title TBA  


Feb 8  Dave Morris  Title TBA  


Feb 22  David Nguyen  Title TBA  
(University of California, Santa Barbara)  


Mar 1  Andrew Fiori  Title TBA  


Mar 8  Amir Akbary  Title TBA  


Mar 15  Speaker TBA  Title TBA  


Mar 22  Speaker TBA  Title TBA  


Mar 29  Nathan Ng  Title TBA  

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Spring  S2008  S2009  S2010  S2012  S2013  S2014  S2015  S2016  S2017  S2018  S2019  S2020 
Click here for a PDF file of abstracts of all talks back to 2007 (approx 385K). 