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 L-functions and a Chebyshev-type bias for zeros
We describe a thin family of Dirichlet L-functions 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 L-functions seems to have a significant and previously undetected bias in distribution of gaps between their zeros. After uncovering this bias, we re-examined the gaps between the zeros of the Riemann zeta-function 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 "Chebyshev-type" 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 L-functions.

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 L-functions and a Chebyshev-type 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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