scholarly journals Auxiliary functions in transcendental number theory

2009 ◽  
Vol 20 (3) ◽  
pp. 341-373 ◽  
Author(s):  
Michel Waldschmidt
Keyword(s):  
Number Theory ◽  
Transcendental Number ◽  
Auxiliary Functions

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

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.

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.

scholarly journals 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

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.

Transcendental Number Theory

1975 ◽  
Vol 59 (410) ◽  
pp. 280
Author(s):  
H. Halberstam ◽  
Alan Baker
Keyword(s):  
Number Theory ◽  
Transcendental Number

scholarly journals Zariski-dense subgroups and transcendental number theory

2005 ◽  
Vol 12 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Gopal Prasad ◽  
Andrei S. Rapinchuk
Keyword(s):  
Number Theory ◽  
Transcendental Number ◽  
Dense Subgroups

scholarly journals O-Minimal Invariants for Discrete-Time Dynamical Systems

2022 ◽  
Vol 23 (2) ◽  
pp. 1-20
Author(s):  
Shaull Almagor ◽  
Dmitry Chistikov ◽  
Joël Ouaknine ◽  
James Worrell
Keyword(s):  
Number Theory ◽  
Dynamical Systems ◽  
Discrete Time ◽  
Program Verification ◽  
Transcendental Number ◽  
Linear Recurrence ◽  
Open Problems ◽  
Linear Dynamical Systems ◽  
Recurrence Sequences ◽  
Positivity Problems

Termination analysis of linear loops plays a key rôle in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination relates to deep open problems in number theory, such as the decidability of the Skolem and Positivity Problems for linear recurrence sequences, or equivalently reachability questions for discrete-time linear dynamical systems. In this article, we introduce the class of o-minimal invariants , which is broader than any previously considered, and study the decidability of the existence and algorithmic synthesis of such invariants as certificates of non-termination for linear loops equipped with a large class of halting conditions. We establish two main decidability results, one of them conditional on Schanuel’s conjecture is transcendental number theory.

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