Classification of integral lattices with large class number
نویسندگان
چکیده
منابع مشابه
Classification of integral lattices with large class number
A detailed exposition of Kneser’s neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program which automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera of `-elementary lattices, for small prime level `; a...
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Acknowledgements I am undoubtedly indebted to my two supervisors, Alf van der Poorten and Hugh Williams. Most students would feel lucky to have one good supervisor whereas I had the privilege of having two excellent mathematicians to guide me. Their help, wisdom and infinite patience has been invaluable, and I am very grateful for it. The Mathematics Department at Macquarie University has provi...
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After a review of the quadratic case, a general problem about the existence of number fields of a fixed degree with extremely large class numbers is formulated. This problem is solved for abelian cubic fields. Then some conditional results proven elsewhere are discussed about totally real number fields of a fixed degree, each of whose normal closure has the symmetric group as Galois group.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1998
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-98-00938-7