Results on the distribution of primes.
We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.
We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents of the -functions of any degree in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
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