One investigates the behavior for R→+∞ of the two-dimensional Dirichlet kernels[Figure not available: see fulltext.], where W⊂ℝ² is a fixed polygon. It is known that[Figure not available: see fulltext.] for any polygon, and[Figure not available: see fulltext.][Figure not available: see fulltext.], if the coordinates of all the vertices of W are rational numbers. It is shown that in the general case the second result is not true: there exists a triangle W such that[Figure not available: see fulltext.].