Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

In some old notes, I found the following conjecture:

Let $\mathbb T$ denote the unit circle and let $\chi:{\mathbb N} \to {\mathbb T}$ be fully multiplicative. Then the L-series $$ L(\chi,s)=\sum_{n=1}^\infty\frac{\chi(n)}{n^s}, $$ defined for ${\rm Re}(s)>1$, cannot be extended to a holomorphic function on $\{ {\rm Re}(s)\ge 0\}$.

Who formulated this conjecture? What related results are known?

share|improve this question
    
What does "fully multiplicative" mean? completely multiplicative? –  Kevin Smith Mar 23 '12 at 9:56
1  
The second question is easy: it is false. See mathoverflow.net/questions/15176/…. The answer to the first question is "We'll never know". Indeed, how are you going to prove that some lost manuscript of Archimedes (or some private letter of Euler, or...) did not contain the full discussion already? –  fedja Mar 23 '12 at 10:08
    
@fedja: Thanks a lot! –  anton Mar 23 '12 at 11:06
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.