Timeline for History of "no positive definite ternary integral quadratic form is universal"?
Current License: CC BY-SA 3.0
12 events
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Feb 13, 2022 at 8:55 | answer | added | Ivan Meir | timeline score: 2 | |
| Sep 15, 2011 at 19:39 | comment | added | Will Jagy | And, for a one-page course on what sort of numbers are not represented by (the genus of) a positive ternary form, zakuski.math.utsa.edu/~kap/Forms/Dickson_Diagonal_1939.pdf | |
| Sep 15, 2011 at 7:11 | comment | added | Franz Lemmermeyer | I think that I can safely say that a result like that does not show up in the literature between Euler and Gauss. A natural place to look, except for Dickson's history, is his book on quadratic forms, or the one by Bachmann in the late 19th century. | |
| Sep 15, 2011 at 4:18 | comment | added | Will Jagy | pages 4-5 of zakuski.math.utsa.edu/~kap/Forms/Kap_Classification_1996.pdf Many other unpublished and published items at zakuski.math.utsa.edu/~kap/forms.html and then four or more variables at zakuski.math.utsa.edu/~kap/more_than_this.html | |
| Sep 15, 2011 at 3:28 | comment | added | Pete L. Clark | @Will: thanks for this latest comment. I am not so up on the literature in this area: could you give a reference to one of the papers where this argument of Kaplansky appears? | |
| Sep 15, 2011 at 1:52 | comment | added | Will Jagy | Let me emphasize that a positive ternary that integrally represents 1,2,3,5 has discriminant no larger than 40. Inequalities show that these are a finite collection, all of which turn out to fail to integrally represent a number below 32. A form with discriminant 41 or larger integrally misses at least one of (1,2,3,5). Kap wrote this out in many places. No Hensel. | |
| Sep 15, 2011 at 1:31 | comment | added | Will Jagy | It seems you should look at B. W. Jones, Transactions of the AMS, volume 33 (1931) pages 92-110. I do not have it. | |
| Sep 14, 2011 at 20:58 | history | edited | Pete L. Clark | CC BY-SA 3.0 |
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| Sep 14, 2011 at 19:52 | history | edited | Pete L. Clark | CC BY-SA 3.0 |
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| Sep 14, 2011 at 19:23 | answer | added | Will Jagy | timeline score: 8 | |
| Sep 14, 2011 at 13:34 | history | asked | Pete L. Clark | CC BY-SA 3.0 |