This Wednesday, one of UIUC's best grad students will be giving a talk entitled "The Birth of Analytic Number Theory" to the local undergrad math club (MATRIX). It will be held at 7pm in Altgeld 245, and should be great. The abstract is below. I **highly** encourage people to attend.

ABSTRACT: In the mid-1700's Euler made the first significant advance in the study of the distribution of prime numbers that had been made since Euclid's proof that there are infinitely many prime numbers. He established what is now known as the Euler product formula and used it to show that the sum of reciprocals of prime numbers diverges. This last result can be interpreted as a statement about how slow the prime numbers thin out. The influence of Euler's paper has been vast and can be felt on much contemporary research in number theory and related areas. In this talk I will derive Euler's product formula and show how Euler proved that the sum of reciprocals of primes diverges. If time permits I will show how he subsequently used his method to establish that the prime numbers are in some sense equally split between the arithmetic progressions 4k + 1 and 4k + 3.

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