MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I once heard a conjecture that a primitive L-function does not have multiple zeros except the central point of the critical strip.

Question:Why it is reasonable to conjecture a primitive L-function does not have multiple zeros except the central point of the critical strip? Is it possible to explain why the central values behave so different?

share|cite|improve this question
    
About why the central point is special: first, from an elementary viewpoint, if the functional equation has sign $+1$ and the $L$-function vanishes at all, then obviously it vanishes doubly, etc. Second, much more seriously, for example the Birch-SwinnertonDyer conjecture predicts that the order of vanishing of an elliptic curve (over $\mathbb Q$) 's $L$-function at the central point is the rank of the free part of rational points of the elliptic curve. Examples are already known where this rank is $>1$. – paul garrett Dec 23 '11 at 18:59
    
That is to say,the multiple zeros carry some arithmetical information we do not fully understand(for a higher degree L-function)? – zy_ Dec 24 '11 at 5:21

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.