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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: | |||
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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. |
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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 ![]() |
Date | Speaker | Title | |
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Jan 18 | everyone | Organizational meeting and problem session | |
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Jan 28 | Micah Milinovich | Irregularities of Dirichlet L-functions and a Chebyshev-type bias for zeros | |
Thursday |
(University of Mississippi) | ||
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Feb 1 | Quanli Shen | Title TBA | |
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Feb 8 | Dave Morris | Title TBA | |
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Feb 22 | David Nguyen | Title TBA | |
(University of California, Santa Barbara) | |||
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Mar 1 | Andrew Fiori | Title TBA | |
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Mar 8 | Amir Akbary | Title TBA | |
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Mar 15 | Speaker TBA | Title TBA | |
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Mar 22 | Speaker TBA | Title TBA | |
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Mar 29 | Nathan Ng | Title TBA | |
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Past semesters: | Fall | F2007 | F2008 | F2009 | F2010 | F2011 | F2012 | F2013 | F2014 | F2015 | F2016 | F2017 | F2018 | F2019 | F2020 |
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). |