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).
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