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Optimization problems for multiplicative functions

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OOEW04 - Structure and Randomness - a celebration of the mathematics of Timothy Gowers

  20+ years ago, Soundararajan and I initiated a study of the spectrum, the range of possible mean values of multiplicative functions which take their values at primes in some given set S. We resolved this question for S=[-1,1], and asked for more general results.   There are several obvious directions to take this—S is the set of mth roots of unity for m>2, or S=[-l,k], or … In this talk I will report on recent progress on these questions in joint works with Kevin Church, Kaisa Matomaki, K. Soundararajan and Daodao Yang.

This talk is part of the Isaac Newton Institute Seminar Series series.

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