0
$\begingroup$

I would like to know whether Langlands' functoriality conjecture implies that the Selberg class coincides with the class of automorphic L-functions and, if so, whether this class is closed under Rankin-Selberg convolution or not.

Many thanks in advance.

$\endgroup$
3
$\begingroup$

The Langlands functoriality conjecture implies that automorphic $L$-functions belong to the Selberg class, but not the other way (i.e. the other direction is not known to follow from this conjecture). Regarding to Rankin-Selberg convolutions, I don't think that this operation has been defined precisely for the Selberg class. There is a subtlety at the ramified primes: one usually refers to the algebraic classification of the underlying local representations, which is itself part of the Langlands program.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ If I'm not mistaken, this operation has been defined for the Selberg class in Murty, M. Ram and Zaharescu, Alexandru (2002), ”Explicit for- mulas for the pair correlation of zeros of functions in the Selberg class”, Forum Math. 14 (2002), no. 1, pp. 65-83. $\endgroup$ – Sylvain JULIEN Jan 31 '16 at 18:24
  • $\begingroup$ may I send you a copy of the latest version of an article of mine dealing with such issues? You can join me at sylvainjul'at'gmail'dot'com. $\endgroup$ – Sylvain JULIEN Jan 31 '16 at 18:32
  • $\begingroup$ @SylvainJULIEN: I don't have any free time to join your project, sorry about this. If your paper gets published, I will be happy to look at it. $\endgroup$ – GH from MO Jan 31 '16 at 18:52
  • $\begingroup$ You can read it there: les-mathematiques.net/phorum/read.php?43,1210447 $\endgroup$ – Sylvain JULIEN Feb 2 '16 at 14:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.