Timeline for Groups related to sum of squares function?
Current License: CC BY-SA 2.5
12 events
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| Jun 7, 2010 at 22:35 | history | edited | Will Jagy | CC BY-SA 2.5 |
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| Jun 7, 2010 at 22:24 | comment | added | Will Jagy | Yes, comment by JSE after my answer to this: mathoverflow.net/questions/3596/… Seems to refer to a different paper, though. | |
| Jun 7, 2010 at 22:16 | comment | added | Will Jagy | Very good. Jordan Ellenberg (JSE) put an answer to one of the questions here on representation numbers for the sum of three squares, or perhaps a comment in case you look for it. It was funny, he said little in a certain paper of his was really new except for the word torsor. | |
| Jun 7, 2010 at 21:48 | comment | added | Dror Speiser | @Will: Great! This article is really interesting. It does connect representations to groups, or more correct, torsors. Note: there's a reference in the question to Hardy's paper. It contains results connecting representations to values of the $L$ function of quadratic number fields. | |
| Jun 7, 2010 at 20:44 | comment | added | Will Jagy | As you like groups, you might look at Ellenberg and Venkatesh arxiv.org/pdf/math/0604232 and the follow-up by Schulze-Pillot, arxiv.org/pdf/0804.2158 although in these the groups may not be the type you want and these focus on existence of representations, rather than counting them when existence is already known. Oh, well. My earlier comment stands as far as my own limited background, I haven't seen anything on five or seven squares that screams number field. | |
| Jun 7, 2010 at 20:13 | comment | added | Dror Speiser | Thanks, the articles are very impressive! I looked over them and reading more carefully now. Just a note, none mention any arithmetic groups. | |
| Jun 7, 2010 at 18:24 | history | edited | Will Jagy | CC BY-SA 2.5 |
bodo lass
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| Jun 7, 2010 at 18:06 | history | edited | Will Jagy | CC BY-SA 2.5 |
cooper
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| Jun 7, 2010 at 8:42 | comment | added | Roland Bacher | You might also want to have a look at the very nice paper of Bodo Lass , Démonstration de la conjecture de Dumont, C. R. Math. Acad. Sci. Paris 341 (2005), no. 12, 713--718. | |
| Jun 7, 2010 at 6:43 | comment | added | Robin Chapman | A paper on five, seven and nine squares is Shaun Cooper's "Sums of five, seven and nine Squares" also in the Ramanujan Journal vol. 6 (2002) 469-490. | |
| Jun 7, 2010 at 3:46 | comment | added | Wadim Zudilin | Here is the link to the paper: dx.doi.org/10.1023/A:1014865816981. There are simpler proofs of the result (probably not mentioned in Milne's paper) by D. Zagier [Math. Res. Lett. 7 (2000) 597--604], K. Ono [J. Number Theory 95 (2002) 253--258], and H.H. Chan and C. Krattenthaler [Bull. London Math. Soc. 37 (2005) 818--826]. | |
| Jun 6, 2010 at 23:09 | history | answered | Will Jagy | CC BY-SA 2.5 |