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Tuesday, April 2, 2024

Posted November 14, 2023
Last modified March 26, 2024

Algebra and Number Theory Seminar Questions or comments?

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Micah Milinovich, University of Mississippi
Biases in the gaps between zeros of Dirichlet L-functions

We describe a family of Dirichlet L-functions that provably have unusual value distribution and experimentally have a significant and previously undetected bias in the distribution of gaps between their zeros. This has an arithmetic explanation that corresponds to the nonvanishing of a certain Gauss-type sum. We give a complete classification of the characters for when 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, so L-functions in our newly discovered family are rare (zero density set amongst primitive characters). If time allows, I will also describe some newly discovered experimental results concerning a "Chebyshev-type" bias in the gaps between the zeros of the Riemann zeta-function. This is joint work with Jonathan Bober (Bristol) and Zhenchao Ge (Waterloo).

Tuesday, April 30, 2024

Posted September 24, 2023
Last modified March 3, 2024

Algebra and Number Theory Seminar Questions or comments?

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom

Ana Bălibanu, Louisiana State University
TBA