Timeline for How many finite subsets in $\mathbb{Z}^d$ have a given sum of squares?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2015 at 18:15 | vote | accept | Vladimir | ||
| Mar 11, 2015 at 14:55 | comment | added | Fedor Petrov | @TheMaskedAvenger my final result is an estimate for logarithm, of course | |
| Mar 11, 2015 at 14:53 | comment | added | The Masked Avenger | This strikes me as too small. In particular, one has a factor of 2^k to account for signs when m is the sum of k nonzero squares. Also, one can pad by zeroes to generate O(k^d) different sets of vectors where each vector has one nonzero component. I expect growth more like exp(m). | |
| Mar 11, 2015 at 14:41 | comment | added | Fedor Petrov | Yes. They are actually close enough by some standard reasoning (function is not too much oscillating.) | |
| Mar 11, 2015 at 14:29 | comment | added | Vladimir | Thanks! So just to be clear - to turn this into a proof we would need to estimate how far the integral is from the sum? | |
| Mar 11, 2015 at 14:29 | vote | accept | Vladimir | ||
| Mar 11, 2015 at 14:55 | |||||
| Mar 11, 2015 at 13:57 | history | answered | Fedor Petrov | CC BY-SA 3.0 |