Timeline for Probing the generalization of the abc conjecture to more than 3 variables
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2014 at 13:09 | comment | added | joro | Isn't it easier to make $x^2+xy+y^2=a^n$ for $n$ sufficiently large and this will give quality close to $4/3$? The gcd will be bounded by $2$. Looks like $n>4$ already gives fixed good quality. | |
| Aug 29, 2014 at 13:04 | comment | added | Felipe Voloch | In the function field case, Mason proved a bound for which the exponent depended exponentially in $n$ and then, Brownawell-Masser and I more or less at the same time proved the result with an exponent quadratic in $n$. In any case, that exponent hasn't moved in nearly 30 years. Browkin and Brzezinski show that it can't be lower than $2n-5$ (unless one excludes a Zariski-closed set, perhaps). It would be very interesting to settle the exponent in the function field case. | |
| Aug 29, 2014 at 11:12 | history | answered | tdw | CC BY-SA 3.0 |