Dirichlet's theorem and L-functions -- Ming-Lun (Eric) Hsieh, November 8, 2004

<p>

	Given a,b two coprime integers, Dirichlet's theorem 
states that there are infinitely many primes of the form 
an+b where n runs through the integers.  To prove this, 
Dirichlet brought up L-functions associated to Dirichlet
characters which generalize Riemann-zeta function by which 
Euler could prove the existence of infinitely many primes, 
and somehow he reduced the problem to showing the 
nonvanishing of these L-functions evaluated at 1.
	In this talk, I would like to explain his reduction in 
detail and sketch how he got the nonvanishing result from 
the knowledge of zeta functions for cyclotomic fields. The 
reference is Serre's book &quot;A course in Arithmetic.&quot;