منابع مشابه
Moments of zeta and correlations of divisor - sums : I Brian
We examine the calculation of the second and fourth moments and shifted moments of the Riemann zetafunction on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enabl...
متن کاملThe divisor function over arithmetic progressions
provided x is sufficiently large. An asymptotic formula of type (1) Df (x; q, a) = (1 +O((log x)))Df (x; q) , in which the error term is smaller than the main term by a suitable power of log x, is good enough for basic applications. More important than the size of the error term is the range where (1) holds uniformly with respect to the modulus q. In this paper we consider the problem for the d...
متن کاملHigher Correlations of Divisor Sums Related to Primes
Abstract. We calculate the triple correlations for the truncated divisor sum λR(n). The λR(n)’s behave over certain averages just as the prime counting von Mangoldt function Λ(n) does or is conjectured to do. We also calculate the mixed (with a factor of Λ(n)) correlations. The results for the moments up to the third degree, and therefore the implications for the distribution of primes in short...
متن کاملMoments of zeta and correlations of divisor-sums: IV
In this series we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begins the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asy...
متن کاملMoments of zeta and correlations of divisor-sums: I.
We examine the calculation of the second and fourth moments and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enab...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2012
ISSN: 0024-6115
DOI: 10.1112/plms/pdr046