Re:Mathematicians clear hurdle in quest to decode primes
by CrushItNerds519 on Friday January 14, 2022 @04:16AM
(#29932271)
As you say, we now know that each standard L-function satisfies a subconvex estimate as its argument varies. This falls short of "solving the subconvexity problem" in two respects.
The first, pointed out already by gavagai691, is that it is not known that "every L-function" is "standard" (this is a major open problem in the Langlands program).
The second is that the general "subconvexity problem" asks for a nontrivial estimate not only for each fixed L-function as its argument varies, but more generally as the L-function itself varies. The general case of the problem remains open.
The first, pointed out already by gavagai691, is that it is not known that "every L-function" is "standard" (this is a major open problem in the Langlands program).
The second is that the general "subconvexity problem" asks for a nontrivial estimate not only for each fixed L-function as its argument varies, but more generally as the L-function itself varies. The general case of the problem remains open.