On the divisor sum function
نویسندگان
چکیده
منابع مشابه
Divisor-sum Fibers
Let s(·) denote the sum-of-proper-divisors function, that is, s(n) = ∑ d|n, d<n d. Erdős–Granville–Pomerance–Spiro conjectured that for any set A of asymptotic density zero, the preimage set s−1(A ) also has density zero. We prove a weak form of this conjecture: If (x) is any function tending to 0 as x→∞, and A is a set of integers of cardinality at most x 1 2 + , then the number of integers n ...
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Abstract. A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1,2,...,| ( ) |} V G such that each edge uv assigned the label 1 if 2 divides ( ) ( ) f u f v + and 0 otherwise. Further, the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial grap...
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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) and we set T 0 E * (t) dt = 3πT /4 + R(T), then we obtain R(T) = O ε (T 593/912+ε), T 0 R 4 (t) dt ≪ ε T 3+ε , and T 0 R 2 (t) dt = T 2 P 3 (log T) + O ε (T 11/6+ε), whe...
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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 it is proved that
متن کاملOn 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 ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1985
ISSN: 0035-7596
DOI: 10.1216/rmj-1985-15-2-399