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 <> or Dave Morris <>.
Talks are usually at noon on Monday. All times are Mountain Time.
                The next talk:

Jan 18
at noon
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 ( or
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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
(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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