Related papers: A Direct Proof of Landen's Transformation
We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…
We describe several families of permutation polynomials obtained using functions with linear translators.
In this paper we consider a transformation $L_a$ of sequences of complex numbers. We find the inverse transformation of $L_a$ as well as the inverse of a related transformation $\tilde{L}_a$. We explore a connection to the binomial…
In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson is true.
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms of Jacobi's triple product identity and Watson's quintuple…
We prove an analogue of the prime number theorem for finite fields.
We present an elementary proof for Ljunggren equation
We present a new, elementary, dynamical proof of the prime number theorem.
I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
Among finite solutions of Sine-Gordon Equation with in phase N=1, we find Modular and Landen transformation between \theta representation and directly integrated solutions of breather and kink. Because of these transformations, we can say…
This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace…
We present an exact asymptotic solution for electron transition amplitudes in an infinite linear chain driven by an external homogeneous time-dependent electric field. This solution extends the Landau-Zener theory for the case of infinite…
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
We introduce a transformation for converting a series in a parameter, \lambda, to a series in the inverse of the parameter \lambda^{-1}. By applying the transform on simple examples, it becomes apparent that there exist relations between…
We use an elementary argument to prove some finite sums involving expressions of the forms $(q)_n$ and $(a;q)_n$ along with inductive formulas for some sequences.
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
We give a new proof of Lucas' Theorem in elementary number theory.
We present a modification of Riesz's construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time simplifying the proofs.
We discuss Jordan's theorem on finite subgroups of invertible matrices and give an account of his original proof.