Multiplicative Functions on Arithmetic Progressions. VII: Large Moduli

2002 ◽  
Vol 66 (1) ◽  
pp. 14-28 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Arithmetic Progressions ◽  
Multiplicative Functions

scholarly journals SMOOTH‐SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE ‐BARRIER

Mathematika ◽  
2017 ◽  
Vol 63 (3) ◽  
pp. 895-918 ◽  
Author(s):  
Sary Drappeau ◽  
Andrew Granville ◽  
Xuancheng Shao
Keyword(s):  
Arithmetic Progressions ◽  
Multiplicative Functions

scholarly journals Pretentious multiplicative functions and the prime number theorem for arithmetic progressions

2013 ◽  
Vol 149 (7) ◽  
pp. 1129-1149 ◽  
Author(s):  
Dimitris Koukoulopoulos
Keyword(s):  
Prime Number ◽  
Elementary Proof ◽  
Counting Function ◽  
Prime Number Theorem ◽  
Arithmetic Progressions ◽  
Multiplicative Functions ◽  
Primes In Arithmetic Progressions

AbstractBuilding on the concept ofpretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

scholarly journals Arithmetic progressions that consist only of reduced residues

2001 ◽  
Vol 26 (10) ◽  
pp. 589-596
Author(s):  
Paul A. Tanner III
Keyword(s):  
Arithmetic Progressions ◽  
Multiplicative Functions ◽  
Elementary Derivation

This paper contains an elementary derivation of formulas for multiplicative functions ofmwhich exactly yield the following numbers: the number of distinct arithmetic progressions ofwreduced residues modulom; the number of the same with first termn; the number of the same with meann; the number of the same with common differencen. Withmand oddwfixed, the values of the first two of the last three functions are fixed and equal for allnrelatively prime tom; other similar relations exist among these three functions.

Multiplicative functions on arithmetic progressions

Mathematika ◽  
1987 ◽  
Vol 34 (2) ◽  
pp. 199-206 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Arithmetic Progressions ◽  
Multiplicative Functions
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