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We report $^{121/123}$Sb nuclear quadrupole resonance (NQR) and $^{51}$Vnuclear magnetic resonance (NMR) measurements on kagome metal CsV$_3$Sb$_5$with $T_{\rm c}=2.5$ K. Both $^{51}$V NMR spectra and $^{121/123}$Sb NQRspectra split after a charge density wave (CDW) transition, which demonstratesa commensurate CDW state. The coexistence of the high temperature phase and theCDW phase between $91$ K and $94$ K manifests that it is a first order phasetransition. At low temperature, electric-field-gradient fluctuations diminishand magnetic fluctuations become dominant. Superconductivity emerges in thecharge order state. Knight shift decreases and $1/T_{1}T$ shows aHebel--Slichter coherence peak just below $T_{\rm c}$, indicating thatCsV$_3$Sb$_5$ is an s-wave superconductor.

s-wave superconductivity in kagome metal CsV$_{3}$Sb$_{5}$ revealed by $^{121/123}$Sb NQR and $^{51}$V NMR measurements