Measurement of the cross sections of e^+e^- K^-^+/^0 at center-of-mass energies between 3. 510 and 4. 914 GeV

Using e^+e^- collision data collected with the BESIII detector at the BEPCII collider at center-of-mass energies between 3. 510 and 4. 914GeV, corresponding to an integrated luminosity of 25 fb^-1, we measure the Born cross sections for the process e^+e^- K^-^+/^0 at thirty-five energy points with a partial-reconstruction strategy. By fitting the dressed cross sections of e^+e^- K^-^+/^0, evidence for (4160) K^-^+ is found for the first time with a significance of 4. 4, including systematic uncertainties. No evidence for other possible resonances is found. In addition, the products of electronic partial width and branching fraction for all assumed resonances decaying into K^-^+/^0 are determined.