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Caltech/UCLA Joint Analysis Seminar

Tuesday, January 5, 2021
4:00pm to 4:55pm
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Online Event
Extreme values of the argument of the zeta function
Alexander Dobner, Department of Mathematics, UCLA,

Let S(t) = 1/(π Im log ζ(1/2+it)). The behavior of this function is intimately connected to irregularities in the locations of the zeros of the zeta function. In particular S(t) measures the difference between the "expected" number of zeta zeros up to height t and the actual number of such zeros. I will discuss what is known about the distribution of S(t) and prove a new unconditional lower bound on how often S(t) achieves large values.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].