Qibin Shen, Shuhui Shi
Published 2014-12-11Version 1
In 1975, [LMQ] listed 7 function felds over fnite felds (up to isomorphism) with positive genus and class number (i.e., the size of the divisor class group of degree zero) one and claimed to prove that these were the only ones such. In [S1], Claude Strirpe found 8th one! In this paper, we fix the argument in [LMQ] to show that this 8th example could have been found by [LMQ] method and is the only one, so that the list is now complete.
A Note on the Mean Value of $L$--functions in Function Fields
Class numbers of ternary quadratic forms
Ternary arithmetic, factorization, and the class number one problem
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