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한국고등과학원 세미나 



[GSNT] Spinor representations of positive definite ternary quadratic forms 

Kyoungmin Kim (성균관대학교 (AORC) ) 
For a positive definite integral ternary quadratic form f, let r(k,f) be the number of representations of an integer k by f. The famous Minkowski Siegel formula implies that if the class number of f is one, then r(k,f) can be written as a constant multiple of a product of local densities which are easily computable. In this talk, we consider the case when the spinor genus of f contains only one class. In this case the above also holds if k is not contained in a set of finite number of square classes which are easily computable. By using this fact, we prove some extension of the results given on the representations of generalized Bell ternary forms and on the representations of ternary quadratic forms with some congruence conditions. This is a joint work with Jangwon Ju and ByeongKweon Oh. 







