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An alternative to the explicit formula and some applications

Posted in
Winston Heap
London Metropolitan University/MPIM
Wed, 2019-12-11 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We describe a possible alternative to the explicit formula and give two applications. The first relates the maximum of the Riemann zeta function on the one-line (and in the critical strip) to the maximum of S(t) - the remainder in the formula for the number of non-trivial zeros of height t. The second is concerned with cancellations of the Mobius function. In particular, we give new conditional upper bounds for partial sums of the Mobius function.

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