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We searched for Tc in a sample of long period variables selected by stellarluminosity derived from Hipparcos parallaxes. Tc, as an unstable s-processelement, is a good indicator for the evolutionary status of stars on theasymptotic giant branch (AGB). In this paper we study the occurrence of Tc as afunction of luminosity to provide constraints on the minimum luminosity for thethird dredge up as estimated from recent stellar evolution models.  A large number of AGB stars above the estimated theoretical limit for thethird dredge up are found not to show Tc. We confirm previous findings thatonly a small fraction of the semiregular variables show Tc lines in theirspectra. Contrary to earlier results by Little et al. (1987) we find also asignificant number of Miras without Tc.  The presence and absence of Tc is discussed in relation to the massdistribution of AGB stars. We find that a large fraction of the stars of oursample must have current masses of less than 1.5 M_{\sun}. Combining ourfindings with stellar evolution scenarios we conclude that the fraction of timea star is observed as a SRV or a Mira is dependent on its mass.Comment: 10 pages, 4 figures, accepted for publication in A&

Technetium and the third dredge up in AGB stars