Integral points on norm-form varieties

AbstractWe study the distribution of integral points on the varieties of the form f1(x1) = ⋯ = fr(xr), where fj, 1 ≤ j ≤ r, is a norm-form associated to an ideal class in a totally complex finite extension of Q

How many orthonormal bases are needed to distinguish all pure quantum states?

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d=2 the answer is three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4 the answer is either three or four. Curiously, the exact number in d=4 seems to be an open problem

Vistas in analytic number theory

With 66 refs.SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman