Timeline for What if the Riemann Hypothesis were false?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2023 at 5:02 | comment | added | Jay Ordway | @GerryMyerson Let's not throw the baby out with the bath water! | |
| Aug 27, 2015 at 16:52 | vote | accept | Craig Feinstein | ||
| Oct 2, 2014 at 11:57 | history | protected | Todd Trimble | ||
| Jul 17, 2013 at 3:00 | review | Close votes | |||
| Jul 17, 2013 at 7:03 | |||||
| Jul 11, 2013 at 23:42 | comment | added | Gerry Myerson | About 10,000 published papers would be rendered vacuous. | |
| Jul 11, 2013 at 22:33 | comment | added | KConrad | Before the work of Heilbronn, Mordell had shown that if infinitely many imaginary quadratic fields have the same class number (any common value) then RH for the Riemann zeta-function is true. Thus if RH is false, any positive integer can be the class number of finitely many imaginary quadratic fields. | |
| Jul 11, 2013 at 22:31 | comment | added | KConrad | In the early 20th century, the proof that the class number of imaginary quadratic fields ${\mathbf Q}(\sqrt{-d})$ for squarefree $d > 0$ tends to $\infty$ as $d \rightarrow \infty$ was based on a two-part argument: Landau showed that it follows from the assumption that GRH is true for the $L$-functions of all imaginary quadratic Dirichlet characters, and then Heilbronn showed that it follows from the assumption that GRH is false for the $L$-function of some imaginary quadratic Dirichlet character. See Ireland and Rosen's number theory book, p. 359. | |
| Jul 11, 2013 at 18:17 | history | made wiki | Post Made Community Wiki by François G. Dorais | ||
| Jul 11, 2013 at 15:32 | history | edited | Benjamin Steinberg |
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| Jul 11, 2013 at 15:20 | answer | added | Stopple | timeline score: 54 | |
| Jul 11, 2013 at 15:17 | review | Close votes | |||
| Jul 11, 2013 at 15:31 | |||||
| Jul 11, 2013 at 15:13 | history | edited | user9072 |
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| Jul 11, 2013 at 15:11 | comment | added | user9072 | If it were false, a consequence would be that the distribution of the primes would have be to be more interesting than currently (generally) believed. This is a bit of a meta answer. But it would be highly interesting if it were false. In that sense RH true is the more "boring" case. | |
| Jul 11, 2013 at 14:57 | history | asked | Craig Feinstein | CC BY-SA 3.0 |