On integers as the sum of a prime and a $k$-th power
نویسنده
چکیده
Abstract. Let Rk(n) be the number of representations of an integer n as the sum of a prime and a k-th power for k ≥ 2. Furthermore, set Ek(X) = |{n ≤ X, n ∈ Ik, n not a sum of a prime and a k-th power}|. In the present paper we use sieve techniques to obtain a strong upper bound on Rk(n) for n ≤ X with no exceptions, and we improve upon the results of A. Zaccagnini to prove Ek(X) ≪k X 1−181 log 2/1250k log . We also briefly outline methods that can significantly improve the latter result to Ek(X) ≪k X 1−1/k .
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ورودعنوان ژورنال:
- CoRR
دوره abs/0908.0554 شماره
صفحات -
تاریخ انتشار 2009