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Local problems with primes I.

The aim of the present and forthcoming papers is to show how certain "local" problems with primes can be reduced to "local" L-norm problems for suitable exponential polynomials. Moreover we show how, in some cases, non-trivial estimates can be obtained for the local L-norm. By local problems with primes we mean problems involving primes in short intervals, whereas by local L-norm of the exponential polynomial