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Unformatted text preview: 4400/6400 PROBLEM SET 7 Recommendation: 4400 students should do at least 4 problems; 6400 students should do at least 6. 7.1) Write out a careful proof of Lemma 6 in the Minkowskis Theorem handout. Especially, say a bit about the change-of-volume properties of the determinant map. Citing a reference or two might be appropriate. 7.2)** Prove Theorem 11 in the Minkowskis theorem handout. (Possible strat- egy: talk to Professor Joseph H.G. Fu.) 7.3) Let R N be a convex body with volume exactly 2 N . (We have seen that need not have a nonzero lattice point.) Show that if is moreover closed , then it does have a nonzero lattice point. 1 Suggestion: Use the fact that for all > 0, the dilate (1 + ) must contain a nonzero lattice point. 7.4)* Prove Theorem 12 in the Minkowksis Theorem handout. 7.5) Prove Lemma 14 (Eulers identity) in the Minkowksis Theorem handout. 7.6) Prove Lemma 16 in the Minkowksis Theorem handout....
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This note was uploaded on 10/26/2011 for the course MATH 4400 taught by Professor Staff during the Spring '11 term at University of Georgia Athens.
- Spring '11
- Number Theory