Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 438.10036
Autor: Erdös, Paul; Babu, Gutti Jogesh; Ramachandra, K.
Title: An asymptotic formula in additive number theory. II. (In English)
Source: J. Indian Math. Soc., New Ser. 41, 281-291 (1977).
Review: [Part I, cf. Acta Arith. 28, 405-412 (1976; Zbl 278.10047)]
Let {bj} be a sequence of integers satisfying 3 \leq b1 < b2 < b3 < ... and sumj = 1oo\frac 1{bj} < oo. Suppose sumbj \leq x1 = 0(\frac x{log x log log x}). Then the authors prove that the equation n = p+t where p is a prime and t is an integer not divisible by any bj has \frac{\alpha n}{log n}+o(\frac n{log n}) solutions and in particular has at least one solution for all sufficiently large n. Also the authors show that if a certain unproved hypothesis holds then the same result can be established under the slightly milder restriction sumbj \leq x1 = o(\frac{x}{log x}).
Classif.: * 11P32 Additive questions involving primes
11N37 Asymptotic results on arithmetic functions
11N35 Sieves
Keywords: Goldbach conjecture; Brun's Sieve; primitive abundant numbers
Citations: Zbl.278.10047
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag