Mathematics Papers
@MathPaper
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New General Mathematics submissions to https://t.co/wBI0Sjzd7o (not affiliated with https://t.co/wBI0Sjzd7o)
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A Note on the Solution of Symmetric Circulant Real Linear Systems.
arxiv.org
A straightforward real-valued solution to symmetric circulant real linear systems of equations is proposed using the Fast Fourier Transform, applicable to both the cases of a non-constant and a...
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Equality of the Casoratian and the Wronsikian for some Sets of Functions and an Application in Difference Equations.
arxiv.org
The Casoratian determinants are very important in the study of linear difference equation, just as the Wronskian determinants are very important in the study of linear ordinary differential...
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On the Representation of Integers as Sums of Limited Prime Powers.
arxiv.org
We present a novel conjecture concerning the additive representation of natural numbers using prime powers. Based on extensive computational verification, we conjecture that every integer n > 23...
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A Note on the Solution of Symmetric Circulant Real Linear Systems.
arxiv.org
A straightforward real-valued solution to symmetric circulant real linear systems of equations is proposed using the Fast Fourier Transform, applicable to both the cases of a non-constant and a...
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Construction and properties of fuzzy-valued fractal interpolation function by using iterated function system.
arxiv.org
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal...
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Construction of fuzzy valued recurrent fractal interpolation functions and their properties.
arxiv.org
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate...
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A study of a family of self-referential sequences.
arxiv.org
We introduce and analyze a three-parameter family of self-referential integer sequences $S(x,y,z)$: starting from $a(1)=x$, each term advances by $y$ when the index $k$ has already appeared as a...
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Optional intervals event, sequential operation and their applications in physics, computer science and applied mathematics.
arxiv.org
In this paper, we introduce algebraic theories such as set theory and group theory into the analysis of event execution order. We propose concepts like "optional intervals event" and "sequential...
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A fully new path to prove Riemann Hypothesis.
arxiv.org
By transforming the Zeta function into a real function through Laplace inverse transformation, an algebraic research paradigm for prime number distribution was established, and important results...
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On the Explicit Expression of an Extended Version of Riemann Zeta Function.
arxiv.org
In this paper, we focus on the explicit expression of an extended version of Riemann zeta function. We use two different methods, Mellin inversion formula and Cauchy's residue theorem, to...
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On recurrence coefficients of classical orthogonal polynomials.
arxiv.org
In Lett. Math. Phys. 114, 54 (2024) and 115, 70 (2025), the author introduces what is presented as a novel method for determining whether a sequence of orthogonal polynomials is "classical", based...
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On the dual valued generalized hypergeometric function and its special cases.
arxiv.org
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters...
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New Insights into Integrals Involving Gaussian Sums.
arxiv.org
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities...
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A classification of restrictive polynomial correspondences.
arxiv.org
In this manuscript, we study a special class of correspondences on $\mathbb{P}^{1} \times \mathbb{P}^{1}$, namely polynomial correspondences. We focus on what we call restrictive polynomial...
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On the Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.
arxiv.org
A new method is presented to obtain a closed form of the generalized Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.
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Imbalance Prime Sieving: Every Prime Gap Is a Result of a M\"obius Imbalance Obstruction.
arxiv.org
We introduce a novel sieve for prime numbers based on detecting topological obstructions in a Möbius-transformed rational metric space. Unlike traditional sieves which rely on divisibility, our...
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A Majorana Relativistic Quantum Spectral Approach to the Riemann Hypothesis in (1+1)-Dimensional Rindler Spacetimes.
arxiv.org
Following the Hilbert-Pólya approach to the Riemann Hypothesis, we present an exact spectral realization of the nontrivial zeros of the Riemann zeta function $ζ(z)$ with a Mellin-Barnes...
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