MEAN VALUES OF ARITHMETIC FUNCTIONS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS IN THE LARGE‐DEGREE LIMIT

Mathematika ◽  
2020 ◽  
Vol 66 (2) ◽  
pp. 373-394
Author(s):  
Ofir Gorodetsky
Keyword(s):  
Large Degree ◽  
Arithmetic Progressions ◽  
Arithmetic Functions ◽  
Mean Values ◽  
Short Intervals

scholarly journals Mean value theorems for a class of density-like arithmetic functions

2020 ◽  
pp. 1-15
Author(s):  
Lucas Reis
Keyword(s):  
Finite Field ◽  
Arithmetic Function ◽  
Field Extension ◽  
Mean Value ◽  
Arithmetic Functions ◽  
Mean Value Theorem ◽  
Primitive Elements ◽  
Mean Values ◽  
Mean Value Theorems ◽  
Nonzero Mean

This paper provides a mean value theorem for arithmetic functions [Formula: see text] defined by [Formula: see text] where [Formula: see text] is an arithmetic function taking values in [Formula: see text] and satisfying some generic conditions. As an application of our main result, we prove that the density [Formula: see text] (respectively, [Formula: see text]) of normal (respectively, primitive) elements in the finite field extension [Formula: see text] of [Formula: see text] are arithmetic functions of (nonzero) mean values.

VIII. On the corrections to be applied to the monthly means of meteorological observations taken at any hour, to convert them into mean monthly values

1848 ◽  
Vol 138 ◽  
pp. 125-139 ◽  
Keyword(s):  
Monthly Means ◽  
Mean Values ◽  
Short Intervals ◽  
Perfect Knowledge ◽  
Royal Observatory ◽  
The Mean ◽  
The Difference ◽  
Meteorological Observations ◽  
Essential Service

One of the most useful results of observations made at short intervals during the day and night, and continued for several years, is the knowledge we thus obtain of the diurnal ranges of the different subjects of investigation, and consequently the difference between the mean values of each element, as deduced from observations at one or more hours daily, and the true mean for the period over which the observations are spread. At the Royal Observatory at Greenwich magnetical and meteorological observations have been taken since the year 1840, as is familiar to the Fellows of this Society. These have been published to the end of the year 1845. The whole of these observations have been made under my immediate superintendence, under the direction of the Astronomer Royal, and I believe that no observations have been made and reduced with greater care or regularity. As the person entrusted with the superintendence of these operations, I have a more perfect knowledge of them than any other person can have; I feel it therefore a duty to communicate their results from time to time, when the doing so promises to be of essential service in promoting the advancement of the subjects of investigation.

Almost-primes in arithmetic progressions and short intervals

1978 ◽  
Vol 83 (3) ◽  
pp. 357-375 ◽  
Author(s):  
D. R. Heath-Brown
Keyword(s):  
Prime Numbers ◽  
Arithmetic Progressions ◽  
Short Intervals ◽  
Almost Primes ◽  
Primes In Arithmetic Progressions ◽  
Image Position

In this paper we shall investigate the occurrence of almost-primes in arithmetic progressions and in short intervals. These problems correspond to two well-known conjectures concerning prime numbers. The first conjecture is that, if (l, k) = 1, there exists a prime p satisfying

scholarly journals On the mean values and distributions of arithmetic functions

1981 ◽  
Vol 40 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Gutti Jogesh Babu
Keyword(s):  
Arithmetic Functions ◽  
Mean Values ◽  
The Mean
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