Can I read Positive Definite Binary Hermitian Forms with Finitely Many Exceptions on EtoBox?

Positive Definite Binary Hermitian Forms with Finitely Many Exceptions by Wai Kiu Chan; Anna Rokicki is a Mathematics article available to read on EtoBox.

What is Positive Definite Binary Hermitian Forms with Finitely Many Exceptions about?

Let E/F be a CM extension of number fields, and L be a positive definite binary hermitian lattice over the ring of integers of E. An element in F is called an exception of L if it is represented by every localization of L but not by L itself. We show that if E/F and a positive integer k are given, then there are only finitely many similarity classes of positive definite binary hermitian lattices with at most k exceptions. This generalizes the corresponding finiteness result by Earnest and Khosravani [A.G. Earnest, A. Khosravani, Representation of integers by positive definite binary hermitian lattices over imaginary quadratic fields, J. Number Theory 62 (1997) 368-374, Theorem 2.2] for the case F = Q. We also prove that for a fixed totally real field F of odd degree over Q, there are only finitely many CM extensions E/F for which there exists a positive definite regular normal binary hermitian lattice over the ring of integers of E.

Who reads Positive Definite Binary Hermitian Forms with Finitely Many Exceptions?

Author

Wai Kiu Chan; Anna Rokicki

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)