Related papers: Generalized Lindemann-Weierstrass and Gelfond-Schn…
In this paper, we prove that an uncountable quantity of real numbers generated by digital pattern sequences gives the transcendental number. This result gives a generalization of Main theorem in Morton and Mourant [MortM], which state that…
Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$…
To decide upon the arithmetic nature of some numbers may be a non-trivial problem. Some cases are well know, for example exp(1) and W(1), where W is the Lambert function, are transcendental numbers. The Tsallis q-exponential, e_q (z), and…
In this paper, we prove that there are uncountable many real transcendental numbers, which are generated by digital pattern sequences. This generalizes the main theorem in Morton and Mourant, which states the existence of countable many…
The Thue-Morse sequence is generalized to the $TM_m$ sequences and two equivalent definitions are given. This generalization leads to transcendental numbers and has Queff\'elec's theorem on Thue-Morse continued fractions as a special case.…
In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…
We prove in particular that the Gorenstein numerical semigroup ring generated by (36,48,50,52,56,60,66,67,107,121,129,135) has a transcendental series of Betti numbers. The methods of proofs are the theory of Golod homomorphism and the…
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We first give a summary of the history of transcendental numbers then use a nice technique by G. Dresden to prove a new transcendental number. In particular, while previous work looked at the last non-zero digit of $n^n$, we consider the…
Using Schmidt's Subspace Theorem, this paper improves and extends an existing transcendence result for sequences of algebraic numbers. The theorems thus produced correspond to a central theorem on the irrationality of sequences due to…
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and…
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term bilinear recurrence relation of fourth order is given in terms of the Weierstrass sigma function for an associated…
It is well known that value at a non-zero algebraic number of each of the functions $e^{x}, \ln x, \sin x, \cos x, \tan x, \csc x, \sec x, \cot x, \sinh x,$ $ \cosh x,$ $ \tanh x,$ and $\coth x$ is transcendental number (see Theorem 9.11 of…
The purpose of this paper is to combine classical methods from transcendental number theory with the technique of restriction to real scalars. We develop a conceptual approach relating transcendence properties of algebraic groups to results…
We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find…
In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we…
Employing the Lagrange inverting series, a solution of the transcendental equation $(x-a)(x-b)=le^{x}$, that can be considered a quadratic generalization of the equation defining Lambert $W$ function, has been found in terms of Bessel…
We study algebraic and transcendental powers of positive real numbers, including solutions of each of the equations $x^x=y$, $x^y=y^x$, $x^x=y^y$, $x^y=y$, and $x^{x^y}=y$. Applications to values of the iterated exponential functions are…
We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…