Abstract
UDC 511
We introduce a new Diophantine inequality with prime numbers. Let
1
<
c
<
10
9
.
We show that, for any fixed
θ
>
1
,
every sufficiently large positive number
N
,
and a small constant
ε
>
0
,
the tangent inequality
|
p
1
c
tan
θ
(
log
p
1
)
+
p
2
c
tan
θ
(
log
p
2
)
+
p
3
c
tan
θ
(
log
p
3
)
-
N
|
<
ε
has a solution in prime numbers
p
1
,
p
2
,
and
p
3
.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference16 articles.
1. R. Baker, Some Diophantine equations and inequalities with primes, Funct. Approx. Comment. Math., 64, № 2, 203–250 (2021).
2. R. Baker, A. Weingartner, A ternary Diophantine inequality over primes, Acta Arith., 162, 159–196 (2014).
3. Y. Cai, On a Diophantine inequality involving prime numbers, Acta Math. Sinica (Chin. Ser.), 39, 733–742 (1996).
4. Y. Cai, On a Diophantine inequality involving prime numbers III, Acta Math. Sinica (Engl. Ser.), 15, 387–394 (1999).
5. Y. Cai, A ternary Diophantine inequality involving primes, Int. J. Number Theory, 14, 2257–2268 (2018).