Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In this paper, a new kind of divisor function D ( 1 ) ( n ) by the nth coefficient of the Dirichlet series was defined and the error term in the asymptotic formula for ∑ n ≤ x D( 1 )( n ).
6 citations
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19 Jan 1981
TL;DR: In this article, the authors proposed a method to detect and separate a string of constant-period pulses from mixed pulses by considering a time interval between two pulses belonging to mixed pulses to be a divisor and performing processing by dividing times from one end pulse to respective pulses by it in sequence.
Abstract: PURPOSE:To detect and separate a string of constant-period pulses from a string of mixed pulses by considering a time interval between two pulses, belonging to mixed pulses, to be a divisor and by performing processing by dividing times from one end pulse to respective pulses by it in sequence CONSTITUTION:A mixed pulse string from terminal 1 is applied via pulse-interval integrating circuit 2 to memory circuit 3 and time intervals from the 1st pulse of the pulse string to respective pulses are stored Among data from circuit 3, the maximum pulse interval is detected 4 and sent to divisor selecting circuit 5 Circuit 5 selects and sends this to dividing circuit 6, which divides by this interval the time intervals up to respective pulses read out from circuit 3, and from the results, a divisibility frequency is detected 7 and sent to divisibility frequency deciding circuit 8 and dividing circuit 6 Once circuit 8 decides that the divisibility frequency does not reach a fixed number, circuit 5 selects a new divisor to repeat the division and when the divisibility reaches the fixed number, a pulse interval selected at that time as the divisor is output as a repetitive frequency, so that circuit 6 removes the pulse string from circuit 3
6 citations
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01 Sep 19796 citations
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TL;DR: In this paper, the authors studied the higher power moments of the error term in the asymptotic formula of the divisor function with congruence conditions d(n; l 1, M 1, l 2, M 2) for a positive integer n.
Abstract: For a positive integer n, the divisor function with congruence conditions d(n; l 1, M 1, l 2, M 2) denotes the number of factorizations n = n 1 n 2, where each of the factors \({n_i\in\mathbb{N}}\) belongs to a prescribed congruence class l i modulo M i (i = 1, 2). In this paper we study the higher power moments of the error term in the asymptotic formula of \({\sum
olimits_{n\leq M_1M_2x}d(n;l_1,M_1,l_2,M_2)}\) .
6 citations
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TL;DR: In this paper, the authors considered the Zsigmondy set Z(X,f,P,D,D) of the sequence defined by the arithmetic intersection of the f-orbit of P with D. Under various assumptions on X, f, D, and P, they used Vojta's conjecture with truncated counting function to prove that the set of points f^n(P) with n in Z(Z,F,P and D) is not Zariski dense in X.
Abstract: A primitive prime divisor of an element a_n of a sequence (a_1,a_2,a_3,...) is a prime P that divides a_n, but does not divide a_m for all m X be a self-morphism of a variety, let D be an effective divisor on X, and let P be a point of X, all defined over the algebraic closure of Q. We consider the Zsigmondy set Z(X,f,P,D) of the sequence defined by the arithmetic intersection of the f-orbit of P with D. Under various assumptions on X, f, D, and P, we use Vojta's conjecture with truncated counting function to prove that the set of points f^n(P) with n in Z(X,f,P,D) is not Zariski dense in X.
6 citations