# Algebra/Number Theory Seminar

The Lindelof hypothesis for primes is equivalent to the Riemann hypothesis

Steven M. Gonek, U Rochester

12:00 PM - 1:00 PM

Hylan 1106A

The classical Lindelof hypothesis is equivalent to a certain estimate for the sums
. We propose that a more general

form of the Lindelof hypothesis is true, one involving similar estimates for sums of the type
where can be a rather general sequence of integers. We support this with various examples and show that when is the sequence of prime numbers, the truth of our conjecture is equivalent to the Riemann hypothesis.
Moreover, if our conjecture holds when is the sequence of primes congruent to , with coprime to , then the Riemann hypothesis holds for all Dirichlet -functions with characters modulo , and conversely.
These results suggest that a general form of the Lindelof hypothesis may be true that is in some sense more fundamental than either the classical Lindelof hypothesis or the Riemann hypothesis.
This is joint work with Sid Graham and Yoonbok Lee.

Event contact: dinesh dot thakur at rochester dot edu

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