All RMS/DC converters based on computational methods obtained by analog multipliers/dividers or log/antilog circuits cannot give accurate
result at zero input signal.
The former should perform a division by zero, the latter should extract ln(0) which is clearly impossible.
Each converter has its own behavior around zero, which results from various parameters: component properties, trimming errors, noise, leakage etc.
See for example the datasheet of the LTC1966 converter, one of the most accurate in monolithic form.
http://www.analog.com/media/en/technical-documentation/data-sheets/1966fb.pdfIt is based on a different calculation method (sigma/delta) but the principle used is the same as normal log/antilog converters.
The graph named "DC Transfer Function Near Zero" (Pg. 7/38) shows the behavior of the circuit for low input voltages:
as you can see every IC has a different behavior around the zero.
Some multimeters patches the problem by zeroing the reading below a minimum limit.
The only detector that (theoretically) does not have this problem is the thermal converter.
On this behavior, see also:
http://www.gellerlabs.com/34461A%20AC%20zero.htm