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### Multiplicative functions

**Colloquium**

Speaker: | Kannan Soundararajan, Stanford University |

Location: | 1147 MSB |

Start time: | Tue, Nov 14 2006, 4:10PM |

A multiplicative function f:N → C is a function satisfying f(mn)=f(m)f(n). Many naturally occuring functions in number theory are multiplicative. Over the last several years, Andrew Granville and I have been studying various features of multiplicative functions. I will discuss some aspects of this work. For example, I will answer the question of how many numbers up to a given number x are quadratic residues (you are free to choose the prime p so as to minimize the answer). As another example, I will discuss character sums and a recent improvement of a classical inequality of Polya and Vinogradov.