Manchester Number Theory Seminar - Winston Heap
| Dates: | 14 March 2023 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Winston Heap
Title: Mean values of the Hurwitz zeta function on the critical line and its value distribution for irrational parameters.
Abstract: It is known that for typical L-functions coming from arithmetic the distribution on the critical line is log-normal and as such the moments are expected to have a certain size. For rational parameters, the Hurwitz zeta function is given by a linear combination of Dirichlet L-functions and thus falls in this category. In this talk, I will discuss a joint work in progress with Anurag Sahay where we show that for irrational parameters of irrationality exponent <3, the Hurwitz zeta function cannot satisfy this distribution. Precisely, we show that the fourth moment is asymptotically 2 times the second moment squared which suggests a Gaussian distribution.
Room: Frank Adams 1
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Frank Adams 1
Alan Turing Building
Manchester
