Timeline for A heuristic for the density of solutions to Diophantine equations
Current License: CC BY-SA 3.0
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| Jun 22, 2011 at 10:46 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Jun 21, 2011 at 22:17 | comment | added | ACL | However, this concerns rational points of bounded height, and not integral points. General asymptotics for integral points on quasi-projective varieties are not yet conjectured. However, in a recent paper, Yuri Tschinkel and myself developed part of what is needed to state such conjectures in general. In particular, we defined convergence factors and established various volume asymptotics. The reference is Igusa integrals and volume asymptotics in analytic and adelic geometry, Confluentes Mathematici 2 (2010), p. 351–429. arXiv:0909.1568. | |
| Jun 21, 2011 at 20:35 | comment | added | George Lowther | Many thanks, that's a very useful answer. I'll have a look through those references. I've already accepted JSE's answer -- unfortunately I can only choose one, and it can be tricky to tell which to accept before properly understanding everything that's being refered to. It sounds like there's some interesting stuff to read about here. | |
| Jun 21, 2011 at 14:19 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Jun 21, 2011 at 11:27 | comment | added | Daniel Loughran | I should also say that if you want a good overview of what Peyre's constant should look like for hypersurfaces, I would recommend reading Section VI.5 of Joerg Jahnel's habilitation thesis, which can be found on his webpage. | |
| Jun 21, 2011 at 10:59 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Jun 21, 2011 at 10:47 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Jun 21, 2011 at 10:39 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
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| Jun 21, 2011 at 10:32 | history | answered | Daniel Loughran | CC BY-SA 3.0 |