Pillars of Transcendental Number Theory

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.

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Commentaire de « A Note on the Internal Logic of Constructive Mathematics. The Gel’fond-Schneider Theorem in Transcendental Number Theory »

Passages à la limite et seuils critiques. Morceaux Choisis/ Selected Papers ◽

10.2307/j.ctv1h0p0n2.22 ◽

2020 ◽

pp. 389-404

Keyword(s):

Number Theory ◽

Transcendental Number ◽

Constructive Mathematics ◽

Internal Logic

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Auxiliary functions in transcendental number theory

The Ramanujan Journal ◽

10.1007/s11139-009-9204-y ◽

2009 ◽

Vol 20 (3) ◽

pp. 341-373 ◽

Cited By ~ 2

Author(s):

Michel Waldschmidt

Keyword(s):

Number Theory ◽

Transcendental Number ◽

Auxiliary Functions

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

International Journal of Number Theory ◽

10.1142/s1793042112500662 ◽

2012 ◽

Vol 08 (04) ◽

pp. 1099-1105 ◽

Cited By ~ 1

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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Set Theory INC# ∞# Based on Innitary Intuitionistic Logic with Restricted Modus Ponens Rule. Hyper Inductive Denitions. Application in Transcendental Number Theory. Generalized Lindemann-Weierstrass Theorem

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2021/v36i830394 ◽

2021 ◽

pp. 70-119

Author(s):

Jaykov Foukzon

Keyword(s):

Number Theory ◽

Set Theory ◽

Intuitionistic Logic ◽

Theoretical Language ◽

Modus Ponens ◽

Transcendental Number ◽

Weierstrass Theorem ◽

Induction Principle ◽

Intuitionistic Set Theory ◽

Intuitionistic Arithmetic

In this paper intuitionistic set theory INC#∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained without any references to Catalan conjecture. Main results are: (i) number ee is transcendental; (ii) the both numbers e + π and e − π are irrational.

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