In any 1-h-minimal valued field of mixed characteristic (0,p), every transcendental definable curve has at most O_epsilon(H^epsilon) rational points of height at most H.
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Counting rational points on transcendental curves in valued fields
In any 1-h-minimal valued field of mixed characteristic (0,p), every transcendental definable curve has at most O_epsilon(H^epsilon) rational points of height at most H.