Introduction to L-series and Dirichlet characters? I'm looking for an introductory text on Dirichlet characters and the L-series of a field K, specifically for quartic extensions of $\mathbb{Q}$.  I have Davenport's Multiplicative Number Theory, Ireland/Rosen, Marcus' Number Fields, and Washington's Cyclotomic Fields, but things seem to be scattered and I was hoping for more concrete examples.  Does anyone have any suggestions?  This graduate student would appreciate any ideas you have!
Thanks!
 A: The last chapter of Fröhlich and Taylor's "Algebraic number theory" covers Dirichlet L-functions. The last section of that chapter contains applications to biquadratic fields (as well as cubic and sextic fields). There are also some "purely algebraic" results on biquadratic fields earlier in the book.
A: Nancy Childress' book on class field theory has a nice chapter, even though it is more or less taken (in parts) from Washington's chapter 3 and 4. 
Lang's "Algebraic number theory" also has a chapter I think. 
Serre's "A course in arithmetic" is also nice. 
Edit: there is a rather thorough introduction to L-functions in Volume 2 of Cohen's Number theory. I haven't seen it myself, but from the table of contents it seems very detailed and from scratch-approach. 
As Kevin mentions Fröhlich-Taylor has a chapter on L-functions, but I find their book a little hard to read. But you might feel differently. 
I'll report back if I think of anything else.
Cheers,
/Daniel
A: Have you looked at Shimura's book Elementary Dirichlet Series and Modular forms? Here is a link to this book on Amazon.
