LIMITING DISTRIBUTIONS OF THE CLASSICAL ERROR TERMS OF PRIME NUMBER THEORY

作者：Akbary Amir; Ng Nathan^*; Shahabi Majid

来源：The Quarterly Journal of Mathematics, 2014, 65(3): 743-780.

DOI：10.1093/qmath/hat059

In this article, we prove a general theorem which establishes the existence of limiting distributions for a wide class of error terms from prime number theory. As a corollary to our main theorem, we deduce previous results of Wintner [On the asymptotic distribution of the remainder term of the prime number theorem, Amer. J. Math. 57 (1935), 534-538], Rubinstein and Sarnak [Chebyshev%26apos;s bias, Experiment. Math. 3 (1994), 173-197] and of Ng [The summatory function of the Mobius function, Proc. London Math. Soc. (3) 89 (2004), 361-389]. In addition, we establish limiting distribution results for the error term in the prime number theorem for an automorphic L-function, weighted sums of the Mobius function, weighted sums of the Liouville function, the sum of the Mbius function in an arithmetic progression and the error term in Chebotarev%26apos;s density theorem.

• 出版日期2014-9