Additive Number Theory of Polynomials over a Finite Field (Oxford Mathematical
This volume is a systematic treatment of the additive number theory of polynomials over a finite field, an area possessing deep parallels with classical number theory. In providing asymptotic proofs of both the Polynomial Three Primes Problem (an analogue of Vinogradov's theorem) and the Polynomial Waring Problem, the book develops the various tools necessary to apply an adelic circle method to a wide variety of additive problems in both the polynomial and classical settings. A key to the methods employed here is that the Generalised Riemann Hypothesis is valid in this polynomial setting. The authors presuppose a familiarity with algebra and number theory as might be gained from the first two years of a graduate course, but otherwise the book is self-contained.
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