Related papers: The Third Trick
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.
We present a general method to obtain asymptotic power series for three kinds of sequences. And we give recurrence relations for determining the coefficients of asymptotic power series for these sequences. As applications, we show how these…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.
We prove an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero, generalising the results postulated in Diekmann, Kaper (1978, Nonlinear Anal. 2(6), 721--737) and Carr, Chmaj (2004, Proc. AMS 132(8),…
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…
In this note we prove an inequality involving primes and the product of consecutive primes.
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a)=ab$, $\sigma(b)=ac$, $\sigma(c)=a$. The prefix of $\mathbb{T}$ of length $n$ is denoted by $\mathbb{T}[1,n]$. The main result is threefold, we give: (1)…
We obtain another proof of Hermite's integral for the Hurwitz zeta function.
We consider the known functional identity on the Weierstrass sigma function. A complete classification of odd entire functions which satisfy the same identity is obtained.
We give a new characterization of generalized B\"uchi sequences (sequences whose sequence of squares has constant second difference $(a)$, for some fixed integer $a$) of length 3 over the integers and a strategy for attacking B\"uchi's n…
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
We show that for most choices of an initial seed $x_0$, the sequence of the first $N$ iterates of $x_0$ under the $3x+1$ map approximately satisfies Benford's law.
We obtain some results related to Romanoff's theorem.
We apply a classic result in Theoretical Computer Science to solve a sticky problem, and give a neat and slick quick proof of half of it
We prove a new cross theorem for separately holomorphic functions.