On the first sign change in Mertens' theorem
The function is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before exp(495.702833165).
On the fractional parts of and related sequences. II
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
On the frequencies of large values of divisor functions
On the function .
On the generalization of the D. H. Lehmer problem II
On the greatest prime divisor of quadratic sequences
On the greatest prime factor of for a prime p and other expressions
On the greatest prime factor of a cubic polynomial.
On the greatest prime factor of (ab + 1) (ac + 1) (bc + 1)
On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)
On the greatest prime factor of an arithmetical progression. II
On the greatest prime factor of
There exist infinitely many integers such that the greatest prime factor of is at least . The proof is a combination of Hooley’s method – for reducing the problem to the evaluation of Kloosterman sums – and the majorization of Kloosterman sums on average due to the authors.
On the greatest prime factor of
On the greatest prime factors of polynomials at integer points
On the height of cyclotomic polynomials
On the hybrid mean value of Cochrane sums and generalized Kloosterman sums
On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
On the independence of σ(ϕ(n)) and ϕ(σ(n))
On the Integers n for which ...(n) = k (II).
On the Integers Relatively Prime to n and a Number-Theoretic Function Considered by Jacobsthal.