Selberg,s Formula
المؤلف:
Apostol, T. M.
المصدر:
Introduction to Analytic Number Theory. New York: Springer-Verlag, 1976.
الجزء والصفحة:
...
19-8-2020
1343
Selberg's Formula
Let 
be a positive number, and define
where the sum extends over the divisors 
of 
, and 
is the Möbius function. Then
 |
(3)
|
(Nagell 1951, p. 286).
For 
, 2, ..., 
is given by 0, 1, 3, 7, 11, 15, 20, 25, ... (OEIS A109507), where 
is the nearest integer function
REFERENCES:
Apostol, T. M. Introduction to Analytic Number Theory. New York: Springer-Verlag, 1976.
Nagell, T. "Further Lemmata. Proofs of Selberg's Formula." §73 in Introduction to Number Theory. New York: Wiley, pp. 279-280 and 283-286, 1951.
Selberg, A. "An Elementary Proof of the Prime Number Theorem." Ann. Math. 50, 305-313, 1949.
Sloane, N. J. A. Sequence A109507 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
