Barrier
المؤلف:
Guy, R. K
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
26-12-2018
1157
Barrier
A number 
is called a barrier of a number-theoretic function 
if, for all 
, 
. Neither the totient function 
nor the divisor function 
has a barrier.
Let 
be an open set and 
, then a function 
is called a barrier for 
at a point 
if
1. 
is continuous,
2. 
is subharmonic on 
,
3. 
,
4. ![<span style=]()
{z in partialU:b(z)=0}={z_0}" src="http://mathworld.wolfram.com/images/equations/Barrier/Inline16.gif" style="height:14px; width:147px" />
(Krantz 1999, pp. 100-101).
REFERENCES:
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 64-65, 1994.
Krantz, S. G. "The Concept of a Barrier." §7.7.9 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 100-101, 1999.
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