Pi, a Transcendental Number

2020 ◽  
pp. 152-160
Author(s):  
Malcolm E Lines
Keyword(s):  
Transcendental Number

scholarly journals Diophantine conditions in small divisors and transcendental number theory

2003 ◽  
Vol 9 (6) ◽  
pp. 1401-1409
Author(s):  
E. Muñoz Garcia ◽  
◽  
R. Pérez-Marco ◽  
Keyword(s):  
Number Theory ◽  
Transcendental Number ◽  
Small Divisors

scholarly journals ON THE TRANSCENDENCE OF SOME INFINITE SERIES

2008 ◽  
Vol 50 (1) ◽  
pp. 33-37 ◽  
Author(s):  
JAROSLAV HANČL ◽  
JAN ŠTĚPNIČKA
Keyword(s):  
Infinite Series ◽  
Transcendental Number ◽  
Random Oscillation ◽  
Special Series ◽  
Divisibility Properties

AbstractThe paper deals with a criterion for the sum of a special series to be a transcendental number. The result does not make use of divisibility properties or any kind of equation and depends only on the random oscillation of convergence.

NOTE ON FOURIER–STIELTJES COEFFICIENTS OF COIN-TOSSING MEASURES

2020 ◽  
Vol 102 (3) ◽  
pp. 479-489
Author(s):  
XIANG GAO ◽  
SHENGYOU WEN
Keyword(s):  
Number Theory ◽  
Lower Bound ◽  
Transcendental Number ◽  
Linear Forms In Logarithms ◽  
Multiplicative Semigroup ◽  
Linear Forms ◽  
Coin Tossing

It is known that the Fourier–Stieltjes coefficients of a nonatomic coin-tossing measure may not vanish at infinity. However, we show that they could vanish at infinity along some integer subsequences, including the sequence ${\{b^{n}\}}_{n\geq 1}$ where $b$ is multiplicatively independent of 2 and the sequence given by the multiplicative semigroup generated by 3 and 5. The proof is based on elementary combinatorics and lower-bound estimates for linear forms in logarithms from transcendental number theory.

Legislating the Transcendental: Von Hirsch's Proportionality

1992 ◽  
Vol 51 (3) ◽  
pp. 530-537
Author(s):  
Nigel Walker
Keyword(s):  
House Of Representatives ◽  
Transcendental Number ◽  
Mathematical Truth

In 1897 the Indiana House of Representatives was persuaded by a mathematician (of sorts) to entertain a bill “introducing a new mathematical truth”. The new truth was a method, or more precisely methods, for computing the value of π. Since π is a transcendental number the methods could at best have achieved an approximation. In fact they yielded several inaccurate values, one as wild as 4. The legislators were doubtful enough to refer the bill to a committee (the Committee on Canals) and, when this reported favourably, to the Committee on Temperance. Eventually they had the sense to defer it sine die.

NON-VANISHING OF DERIVATIVES OF L-FUNCTIONS ATTACHED TO HILBERT MODULAR FORMS

2012 ◽  
Vol 08 (04) ◽  
pp. 1099-1105 ◽  
Author(s):  
NAOMI TANABE
Keyword(s):  
Number Theory ◽  
Modular Forms ◽  
Critical Value ◽  
Transcendental Number ◽  
Hilbert Modular Forms ◽  
Hilbert Modular ◽  
Derivatives Of

This paper is to show a non-vanishing property of the derivative of certain L-functions. For certain primitive holomorphic Hilbert modular forms, if the central critical value of the standard L-function does not vanish, then neither does its derivative. This is a generalization of a result by Gun, Murty and Rath in the case of elliptic modular forms. Some applications in transcendental number theory deduced from this result are discussed as well.

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