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Multiplicative functions (and pretentions)

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How many prime factors does a typical integer have? How many distinct numbers are there in the n-by-n times tables? How many primes are there in a given arithmetic progression? Can one analytically continue L-functions defined by counting the number of solutions to equations mod p?

All of these questions, naturally arising in number theory, lead to the subject of the distribution of multiplicative functions. In this lecture we will review some of the key results in this area, re-interpreting them in terms of the notion of “pretentiousness”, as developed by Soundararajan and the speaker.

This talk is part of the Kuwait Foundation Lectures series.

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