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We exhibit central simple algebras over the function field of a diagonalquartic surface over the complex numbers that represent the 2-torsion part ofits Brauer group. We investigate whether the 2-primary part of the Brauer groupof a diagonal quartic surface over a number field is algebraic and givesufficient conditions for this to be the case. In the last section we give anobstruction to weak approximation due to a transendental class on a specificdiagonal quartic surface, an obstruction which cannot be explained by thealgebraic Brauer group which in this case is just the constant algebras.

Diagonal quartic surfaces and transcendental elements of the Brauer group