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Explore optimization problems for multiplicative functions in number theory through this mathematical lecture by Andrew Granville from the Simons Foundation. Examine extreme behaviors of multiplicative functions to better understand their typical patterns, with Halasz's theorem serving as a foundational example. Discover explicit bounds in generalized settings for multiplicative functions whose prime values include kth roots of unity and values within fixed integer intervals [-m,m] where m≥1. Learn about improvements to the uniformity issues in Halasz's theorem for k-bounded multiplicative functions at primes. Gain insights from collaborative research with Kaisa Matomäki, K. Soundararajan, Kevin Church, and Daodao Yang, presented as part of the MPS Conference on Universal Statistics in Number Theory.
