The Hermite constant and its generalizations
The majority of the values for the Hermite constant and its generalizations, namely the dual Hermite constant, the Rankin constant and the Bergé-Martinet constant, have yet to be found. This thesis initiates an exploration into the missing values for these constants. A novel contribution is made by...
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Nanyang Technological University
2023
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sg-ntu-dr.10356-1720992023-11-27T15:35:52Z The Hermite constant and its generalizations Oh, Chun Rong Frederique Elise Oggier School of Physical and Mathematical Sciences Frederique@ntu.edu.sg Science::Mathematics::Number theory The majority of the values for the Hermite constant and its generalizations, namely the dual Hermite constant, the Rankin constant and the Bergé-Martinet constant, have yet to be found. This thesis initiates an exploration into the missing values for these constants. A novel contribution is made by establishing a lower bound for the Rankin constant γn,2 with the lattice Dn. Using this lower bound, we have narrowed down the list of interesting lattices in dimensions 5, 7, and 9 with potential to achieve γn,2 for n = 5, 7, 9. Conjectures are presented for the values of γ5,2, γ7,2, and γ9,2. Future endeavors could concentrate on proving these conjectures. Bachelor of Science in Mathematical Sciences 2023-11-27T01:52:26Z 2023-11-27T01:52:26Z 2023 Final Year Project (FYP) Oh, C. R. (2023). The Hermite constant and its generalizations. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/172099 https://hdl.handle.net/10356/172099 en MH4900 application/pdf Nanyang Technological University |
| institution |
Nanyang Technological University |
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NTU Library |
| continent |
Asia |
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Singapore Singapore |
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NTU Library |
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DR-NTU |
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English |
| topic |
Science::Mathematics::Number theory |
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Science::Mathematics::Number theory Oh, Chun Rong The Hermite constant and its generalizations |
| description |
The majority of the values for the Hermite constant and its generalizations, namely the dual Hermite constant, the Rankin constant and the Bergé-Martinet constant, have yet to be found. This thesis initiates an exploration into the missing values for these constants. A novel contribution is made by establishing a lower bound for the Rankin constant γn,2 with the lattice Dn. Using this lower bound, we have narrowed down the list of interesting lattices in dimensions 5, 7, and 9 with potential to achieve γn,2 for n = 5, 7, 9. Conjectures are presented for the values of γ5,2, γ7,2, and γ9,2. Future endeavors could concentrate on proving these conjectures. |
| author2 |
Frederique Elise Oggier |
| author_facet |
Frederique Elise Oggier Oh, Chun Rong |
| format |
Final Year Project |
| author |
Oh, Chun Rong |
| author_sort |
Oh, Chun Rong |
| title |
The Hermite constant and its generalizations |
| title_short |
The Hermite constant and its generalizations |
| title_full |
The Hermite constant and its generalizations |
| title_fullStr |
The Hermite constant and its generalizations |
| title_full_unstemmed |
The Hermite constant and its generalizations |
| title_sort |
hermite constant and its generalizations |
| publisher |
Nanyang Technological University |
| publishDate |
2023 |
| url |
https://hdl.handle.net/10356/172099 |
| _version_ |
1783955527392296960 |