Fluctuations in galaxy counts: A new test for homogeneity vs. fractality

Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study of galaxy distribution both in redshift and magnitude space. Fluctuations in the counts of galaxies, in a fractal distribution, are of the same order of the average number at all scales as a function of redshift and magnitude. We point out that the study of these kinds of fluctuations can be a powerful test to understand the nature of galaxy clustering at very large scales.