arXiv subjects
Publications and source records attributed to Kobi Snitz.
In this paper we establish a formula for the average of representation numbers of ternary quadratic forms in a spinor genus over a totally real number field. The significant fact about the formula is the fact that it is given in terms of local quantities. Such a formula has already been established by Kneser, Hsia, and Schulze-Pillot, by a different method.
This paper describes the lifting of automorphic characters of $\GO(3)(\A)$ to $\SLT(\A)$. It does so by matching the image of this lift with the lift of automorphic characters from $\GO(1)(\A)$ to $\SLT(\A)$. Our matching actually gives a matching of individual automorphic forms, and not just of representation spaces. Let $\V$ be a $3-$ dimensional quadratic vector space and $\U$ a certain $1-$ dimensional quadratic space. To an automorphic form $I_{\V}(χ,ϕ)$ determined by the Schwartz function $ϕ\in \Sc(\V(\A))$ in the lift of the character $χ$ we match an automorphic form $I_{\U}(μ,ϕ_{0})$ determined by the Schwartz function $ϕ_{0}\in \Sc(\U(\A))$ in the lift of the character $μ$. Our work shows that, the space $\U$ is explicitly determined by the character $χ$. The character $μ$ is explicitly determined by the space $\V$ and the function $ϕ_{0}$ is given by an orbital integral involving $ϕ$.