Let Q(x) be the number of square-full numbers not exceeding x, x is a suffciently large positive number. Assuming the Riemann hypothesis to be tenable, an asymptotic formula of Q(x) with a new error is obtained.
This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of...This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of that theorem will be obtained.展开更多
Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（...Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986展开更多
Let x be a large real number, p, p' be primes, and suppose P2 denotes an almost prime with at most two-prime factors counted with multiplicity. It is conjectured thatwhile in this paper it is shown that, for x suf...Let x be a large real number, p, p' be primes, and suppose P2 denotes an almost prime with at most two-prime factors counted with multiplicity. It is conjectured thatwhile in this paper it is shown that, for x sufficiently large, there holds展开更多
文摘Let Q(x) be the number of square-full numbers not exceeding x, x is a suffciently large positive number. Assuming the Riemann hypothesis to be tenable, an asymptotic formula of Q(x) with a new error is obtained.
文摘This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of that theorem will be obtained.
文摘Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
文摘Let x be a large real number, p, p' be primes, and suppose P2 denotes an almost prime with at most two-prime factors counted with multiplicity. It is conjectured thatwhile in this paper it is shown that, for x sufficiently large, there holds
