Timeline for Clarification on the weak BSD conjecture
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2018 at 10:14 | comment | added | Watson | K. Conrad also wrote an answer here related to these results. | |
| Jun 5, 2016 at 20:23 | vote | accept | CommunityBot | ||
| May 24, 2016 at 16:35 | comment | added | David E Speyer | See also Kuo and Murty mast.queensu.ca/~murty/Kuo-Murty-CJM.pdf | |
| May 24, 2016 at 16:32 | comment | added | David E Speyer | In general, Keith's paper is very clear and pretty; I recommend it. | |
| May 24, 2016 at 16:32 | comment | added | David E Speyer | Regarding the converse: Let $\alpha_p$ and $\beta_p$ be the Frobenius eigenvalues and set $\psi_E(x) = \sum_{p^k < x} (\alpha_p^k + \beta_p^k) \log p$. Keith Conrad math.uconn.edu/~kconrad/articles/eulerprod.pdf (Theorem 1.3) shows that $f_E(x) \sim C (\log x)^r$ is equivalent to (ii) together with $\psi_E(x) = o(x \log x)$, while GRH is equivalent to $\psi_E(x) = O(x (\log x)^2)$, so the Euler product condition appears stronger. (Of course, it is possible someone could find some bootstrapping argument which shows the $o(x \log x)$ and $O(x (\log x)^2)$ bounds are equivalent.) | |
| May 24, 2016 at 16:27 | history | answered | Jeremy Rouse | CC BY-SA 3.0 |