A Cramer type large deviation result for student's t-statistic

Let X, X-1, X-2,... be independent and identically distributed random varia bles with a finite third moment. and let T-n be the Student's t-statistic. This paper shows that lim(n-->infinity) P(T-n > x)/P(t(n) > x) = 1 holds un iformly in 0 less than or equal to x less than or equal to o(n(1/6)), where t(n) has a t-distribution with n - 1 degrees of freedom. An example is als o given to show that a finite third moment is necessary for this result.