Timeline for what is the equivalent of the Euler constant for higher dimensional lattices
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2015 at 22:42 | comment | added | paul garrett | Do you in fact want what you literally asked, or do you actually want something about the Laurent expansion of the corresponding generalized Epstein zeta function at the leading pole? | |
| Dec 16, 2015 at 21:06 | answer | added | David E Speyer | timeline score: 10 | |
| Dec 16, 2015 at 20:06 | answer | added | Matt Young | timeline score: 11 | |
| Dec 16, 2015 at 16:28 | comment | added | David E Speyer | Added automorphic-forms tag, since we are talking about a function on $SL_d(\mathbb{R})$ which is clearly invariant for the right $SL_d(\mathbb{Z})$ action and the left $SO_d(\mathbb{R})$ action. If only we had something like a holomorphicity condition... | |
| Dec 16, 2015 at 16:26 | history | edited | David E Speyer |
edited tags
|
|
| Dec 15, 2015 at 13:45 | history | edited | Joe Silverman | CC BY-SA 3.0 |
Changed to omit $\gamma=0$. Also improved some formatting.
|
| S Dec 15, 2015 at 12:55 | comment | added | user84131 | Then this is almost the integral over a big ball of radius $R$, up to $o (1) $ minus the integral over $D $ (for $\gamma =0$), hence the formula. | |
| S Dec 15, 2015 at 12:55 | comment | added | user84131 | Well. I don't have a reference. However, if you take a fundamental domain $D $ for the lattice, assuming it is compact, and invariant by $x\to -x $, then one can compare each tem with the integral of $|x|^{-d}$ over some $D+\gamma$. Now thanks to the symmetry of $D$, this involves an integral remainder with only the hessian of $|x|^{-d}$, that decreases fast enough for the sum to be convergent. So up to a constant and $o(1)$, the sum is the integral of the function over the reunion of $\gamma+D $. (continued in next comment) | |
| Dec 15, 2015 at 4:56 | comment | added | Igor Rivin | What is a reference for the existence of $c_1, c_2?$ | |
| Dec 14, 2015 at 22:59 | review | First posts | |||
| Dec 14, 2015 at 23:19 | |||||
| Dec 14, 2015 at 22:56 | history | asked | Yannick Bonthonneau | CC BY-SA 3.0 |