Representation Numbers of Spinor Regular Ternary Quadratic Forms


Recently Earnest and Haensch (2019) established that there are exactly twenty-nine (classes of) spinor regular primitive positive-definite integral ternary quadratic forms, which are not regular. In this paper we determine explicit formulas for the representation numbers of the twenty-seven of these ternary quadratic forms, which are alone in their spinor genus. For the remaining two spinor regular forms, which are not alone in their genus, we determine their representation numbers for even positive integers. As a consequence of our formulas we are able to determine exactly which positive integers are represented by the twenty-seven ternary quadratic forms alone in their spinor genus. The integers represented by six of these forms had been found by Lomadze in 1977 and three of them by Berkovich in 2015, one form of which had already been treated by Lomadze. Our method is a new approach and quite different from the methods of said authors.

INTEGERS 21 (2021), A99