On number theoretic conjecture of positive integral points in 5-dimension tetrahedron and a sharp estimate of Dickman–De Bruijn function

2014 ◽  
Vol 16 (9) ◽  
pp. 1937-1966 ◽  
Author(s):  
Ke-Pao Lin ◽  
Xue Luo ◽  
Stephen Yau ◽  
Huaiqing Zuo
Keyword(s):  
Sharp Estimate ◽  
Integral Points ◽  
De Bruijn

scholarly journals On the Boundary Dieudonné–Pick Lemma

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov
Keyword(s):  
Fixed Point ◽  
Interior Point ◽  
Sharp Estimate ◽  
General Boundary ◽  
Extremal Functions ◽  
Angular Derivative ◽  
Additional Information ◽  
Carathéodory Theorem ◽  
Class Of Functions ◽  
Boundary Fixed Point

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.

scholarly journals On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song
Keyword(s):  
Zeta Function ◽  
Rational Number ◽  
Riemann Zeta Function ◽  
Rational Numbers ◽  
Critical Strip ◽  
Integer Part ◽  
Integral Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .

scholarly journals Integral points on hyperelliptic curves

2008 ◽  
Vol 2 (8) ◽  
pp. 859-885 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek ◽  
Michael Stoll ◽  
Szabolcs Tengely
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points
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