Mean values for a class of arithmetic functions in short intervals
نویسندگان
چکیده
منابع مشابه
Arithmetic Progressions of Primes in Short Intervals
Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: If N is sufficiently large and M is not too small compared with N , then the primes in the interval [N, N + M ] contains many arithmetic progressions of length k.
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Mean values of multiplicative functions
Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...
متن کاملOn the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class
We establish the equivalence of conjectures concerning the pair correlation of zeros of L-functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston and Montgomery [‘Pair correlation of zeros and primes in short intervals’, Analytic number theory and Diophantine problems (Stillwater, 19...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2019
ISSN: 0025-584X,1522-2616
DOI: 10.1002/mana.201800276