It has recently been shown that a knowledge of the zeros of a forward elastic scattering amplitude could be used to derive new modified dispersion relations. Using the phase representation, we show that the forward crossing-even KN amplitude probably has six zeros in the complex ω (kaon lab energy) plane. Two of these zeros can be very accurately determined from low-energy scattering data. The modified dispersion relations derived using the knowledge of these zeros yield information on the high-energy parameters, and in general provide a consistency test of the presently available data. The infinite-energy total cross section estimated from a dispersion sum rule is about 15.5 mb, in fair agreement with the experimental total cross section of about 17.3 mb at 20 BeV.