Junior Colloquium
                         
                   Thursday April 12, 2012, 3:35 pm
                    Ayres 4th floor colloquium room

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    Pizza will be served before the talk at 3:15 pm, Ayres 4th floor

                          All are welcome!

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       Dr. Daniel Fiorilli, Princeton Institute for Advanced Study



                     Races between prime numbers

 In a 1853 letter to Fuss, Chebyshev made the remark that there seem
 to be more primes of the form 4n+3 than of the form 4n+1. If we compute
 the (normalized) difference between these two kinds of primes up to x,
 and make a graph of this quantity with x varying, then we get the figure
 which is shown here. What one remarks is that the difference is almost
 always positive, confirming Chebyshev's assertion. Interestingly, the
 statement in Chebyshev's letter is equivalent to the Riemann hypothesis
 for a certain zeta function; in fact the whole subject of prime number
 races is highly dependent on the zeros of zeta functions. The goal of
 the present talk will be to give a taste of the subject, focusing on
 the amusing facts.

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