Timeline for Short Diophantine definition of the sum-of-divisors function (using less than 100 variables)?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2018 at 22:49 | comment | added | user44143 | @YaakovBaruch, if we’re in the realm of remote possibilities, why not search for a proof instead? With an elegant statement in exponential-Diophantine terms, a strong theorem-prover for such statements, and a good search algorithm, one can always hope. | |
| Jan 19, 2018 at 22:01 | comment | added | user44143 | @EmilJeřábek, thanks; that answers the question as stated. I had in mind something with degree < 10, variables < 100, coefficients < 1000, but it never occurred to me that people would use polynomials so wild in so many ways. | |
| Jan 19, 2018 at 17:53 | comment | added | Emil Jeřábek | Jones, Universal Diophantine Equation, lists various variables–degree possibilities in Thm. 4; it shows that small number of variables and small degree are simultaneously possible (around 25). Also, he mentions on the next page that one can write a universal Diophantine equation of arithmetic circuit complexity $<100$ (i.e., the number of additions and multiplications). | |
| Jan 19, 2018 at 9:36 | comment | added | Yaakov Baruch | (For slower types like me: IIRC="if I recall correctly".) Now, even if the function in question, or RH, or other conjectures, where encoded by a Diophantine equation with only tens of variables and not huge degree, what would that be useful for? Could it remotely, conceivably, be more practical to look for counterexamples that way than directly in the encoded problem? | |
| Jan 19, 2018 at 8:19 | comment | added | joro | IIRC there are universal diophantine equations in only tens of variables, but enormous degree. | |
| Jan 19, 2018 at 3:54 | history | asked | user44143 | CC BY-SA 3.0 |