Department of

Mathematics


Seminar Calendar
for Number Theory Seminar events the year of Friday, January 15, 2021.

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Tuesday, February 16, 2021

11:00 am in Zoom,Tuesday, February 16, 2021

Landau-Siegel zeros and central values of L-functions

Kyle Pratt (Oxford)

Abstract: Researchers have tried for many years to eliminate the possibility of Landau-Siegel zeros---certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of $L$-functions at the central point.