The Möbius function and the residue theorem

✍ Scribed by Brian Conrad; Keith Conrad

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 250 KB
• Volume: 110
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.06.018

✦ Synopsis

A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z[T ] has infinitely many prime values unless there is a local obstruction. Replacing Z

where is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples.