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Document Type
Presentation
Location
Bryant Hall 209
Start Date
20-5-2019 2:30 PM
End Date
20-5-2019 3:30 PM
Description
Updated time
Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel 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 Dirichlet L-functions at the central point.
Recommended Citation
Pratt, Kyle, "Landau-Siegel zeros and their illusory consequences" (2019). NSF-CBMS Conference: L-functions and Multiplicative Number Theory. 18.
https://egrove.olemiss.edu/cbms2019/2019/schedule/18
Kyle Pratt Video
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Landau-Siegel zeros and their illusory consequences
Bryant Hall 209
Updated time
Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel 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 Dirichlet L-functions at the central point.