منابع مشابه
On the Riemann Zeta-function and the Divisor Problem Ii
Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain ∫ T 0 |E(t)| dt ≪ε T 2+ε and ∫ T 0 |E∗(t)| 544 75 dt ≪ε T 601 225 . It is also shown how bounds for moments of |E∗(t)| lead to bounds for moments of |ζ( 1 2 ...
متن کاملNotes Relating to Newton Series for the Riemann Zeta Function
This paper consists of the extended working notes and observations made during the development of a joint paper[?] with Philippe Flajolet on the Riemann zeta function. Most of the core ideas of that paper, of which a majority are due to Flajolet, are reproduced here; however, the choice of wording used here, and all errors and omissions are my own fault. This set of notes contains considerably ...
متن کاملq-Riemann zeta function
We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)= ∑∞ n=1(qn(s−1)/[n]s), 0< q < 1, s ∈ C. In this paper, we give q-Bernoulli numbers which can be viewed as interpolation of the above q-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some...
متن کاملThe Riemann Zeta-Function and Hecke Congruence Subgroups. II
which was scantly touched on in [9]. We shall proceed with an arbitrary A to a considerable extent but later restrict ourselves to the situation where αn is supported by the set of square-free integers. This is solely to avoid certain technical complexities pertaining to Kloosterman sums associated with Hecke congruence subgroups which do not appear particularly worth dealing with thoroughly, f...
متن کاملSome Identities for the Riemann Zeta-function Ii
Several identities for the Riemann zeta-function ζ(s) are proved. For example, if φ1(x) := {x} = x− [x], φn(x) := ∫ ∞ 0 {u}φn−1 ( x u ) du u (n ≥ 2), then ζn(s) (−s) = ∫ ∞ 0 φn(x)x −1−s dx (s = σ + it, 0 < σ < 1) and 1 2π ∫ ∞ −∞ |ζ(σ + it)| (σ + t) dt = ∫ ∞ 0 φ n (x)x dx (0 < σ < 1). Let as usual ζ(s) = ∑ ∞ n=1 n −s (Re s > 1) denote the Riemann zeta-function. This note is the continuation of t...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1999
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-91-4-351-365