Binary problems. The spectral approach

This is the first part of a paper on the Goldbach binary problem. For the Möbius function, an arithmetic analog of the Heisenberg noncommutativity is introduced. With the help of this analog, the binary problem is expressed in terms of the mean for Kloosterman sums. In the second part, this mean will be expressed in terms of spectral estimates that yield a solution of the binary problem. ©2000 Kluwer Academic/Plenum Publishers.