## Futbol 5.0 Edicion Oro 📦

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7.6 years ago (2011-08-05) by.NIFTYFUTURE For the latest news, events and updates from Sportsbooks across Australia.
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7.6 years ago.Q:

When are the Riemann Hypothesis and the Strong Converse Problem equivalent for the large sieve?

[Update: this question was edited to be a bit more proper, it is now an examination of the difference between the known results for the Riemann Hypothesis and the Strong Converse Problem.] I know that the Strong Converse Problem for the large sieve has been proved as soon as the Riemann Hypothesis is assumed, and also as soon as the Riemann Hypothesis is proved for the Dirichlet L-functions.
Can one tell me which statement is stronger?
Related references:

A:

The strong converse problem for the large sieve is known for
$$L(s, \chi) = \sum_{p \leq X} \chi(p)p^{ -s}, \quad \mbox{Re}(s) > 1, \quad \chi(p) = \left\{ \begin{array}{cc} 1 & p = 1, \\ -1 & p eq 1 \end{array} \right.$$
where $X$ is allowed to be zero, and $X$ very large. The point is that if $\sigma > \sigma_0,$ then $L(s, \chi) \ll_\sigma X^\sigma$ (here we mean that \$|L(s, \chi)| \ll_\sigma X^\s

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