Carlos Hernan Lopez Zapata

Carlos Hernan Lopez Zapata
Universidad Pontificia Bolivariana · Facultad de Ingeniería Eléctrica

Master of Engineering
Focused on special problems in number theory and analysis. Flint/Cookson-Hills/Borwein/Bailey series /Riemann Hypothesis

About

13
Publications
4,723
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1
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Citations since 2017
8 Research Items
0 Citations
201720182019202020212022202301234567
201720182019202020212022202301234567
201720182019202020212022202301234567
201720182019202020212022202301234567
Introduction
- Findings 2022:Flint-Cookson-Hills series advances (proofs) - 2021 New formula for the Euler-Mascheroni and Lugo constants based on the calculation of the Jensen coefficients and also the Taylor's and Turan's for the Taylor series of the Riemann Xi-function and Even Derivatives of the Xi function at (s=1/2) based on the non-trivial zeros and Jensen coeff. Assertion of the Riemann Hypothesis' consequences and the hyperbolicity of the Jensen polynomials for the Taylor series of Xi at s=1/2 +ti.
Additional affiliations
January 2005 - April 2007
Universidad Pontificia Bolivariana
Position
  • Researcher
Description
  • Researcher in Optical Metrology
Education
January 2001 - April 2007
Universidad Pontificia Bolivariana
Field of study
  • Electronics engineering, DSP, automation and Optical Metrology

Publications

Publications (13)
Preprint
The Flint-Hills series remains as an unsolved problem in analysis because there are no known methods to deal with the convergence of that series. Authors like Alekseyev (2011) connected this question to the irrationality measure of π, that 𝜇(𝜋) > 2.5 would imply divergence of the Flint-Hills series...
Research Proposal
(-Li-1(k) D2 + Li-2 (k) D3 -Li-3 (k) D4 +.....)g(x) = ? where D 2, D3 , .... are the n-derivatives that affects the function g(x) in x. Being g(x) a continues function, which can be evaluated after their derivatives at x, for a value x=a (e.g., a=0) and comes from a model of Taylor series coefficients. Is it related to a known operator or is it a...
Research Proposal
Are we dealing with the era of the "Li-Taylor series" when facing hard unsolved series like the Flint, Borwein, Bayley, Cookson's? This is a model of a curious and amazing operator (whose deduction comes from previous ideas I am not describing totally here, but by a new paper soon), because there will come a season for that. I believe sincerely in...
Research
I am investigating the not evident relationship between the special functions: polylogarithms (Li function), Hurwitz zeta function, Riemann zeta function, Harmonic numbers, digamma, trigramma, Bernoulli numbers, and more in order to prepare a new branch in mathematical analysis that leads to solve pending questions about convergence of hard mathema...
Research Proposal
Full-text available
The Euler-Mascheroni constant is calculated by three novel representations over these sets respectively: 1) Turán moments, 2) coefficients of Jensen polynomials for the Taylor series of the Riemann Xi function at s = 1/2 + i.t and 3) even coefficients of the Riemann Xi function around s = 1/2. These findings support the acceptance of the property o...
Article
In the systems of reconstruction 3D of structured light or interferometric, the spatial phase unwrapping by traditional methods constitutes a difficult problem to solve. The inherent noise to the surface, low visibility of the fringes patterns or the computational method for fringe pattern analysis can affect the discontinuous phase map, producing...
Article
Some interesting 3‐D parameters how: amplitude parameters, spatial parameters, hybrid parameters and functional parameters; are presented in this paper for characterizing surface topography of a steel plate in the carbon (A36), which was subjected to process of corrosion. The surface will be reconstructed with the technique of laser triangulation...
Article
In the perfilometry by means of structured light there are two techniques that are the most used: fringe projection and Moiré. The reconstruction of the object surface with inherently discontinuous or prominent slopings, is usually a difficult problem by using standard phase unwrapping technique i.e. the spatial unwrapping. The alternative of spati...
Conference Paper
This work presents a comparative study between the methods of spatial unwrapping by means of reliability parameter and modified temporal unwrapping as a solution to the phase discontinuities presents in surface perfilometry by fringe projection.
Article
The reconstruction of the object surface with inherently discontinuous regions is usually a difficult problem by using standard phase unwrapping technique i.e. the spatial unwrapping. To recover the range data of such a surface, Huntley and Saldner recently proposed a temporal phase unwrapping procedure (TPUP) and Peng X. et al. based on their work...

Questions

Questions (31)
Question
I have a series defined by the sequence given by the function {(log(f(n)))^(1/n^3)} from n=1 to infinite. f(n) is well defined to lead a proper analysis of boundedness of partial sums(never increasing till infinite).
I ask if the integral of the expression: {(log(f(x)))^(1/x^3) } evaluated between the limits of the integrals: x=1 till x= Infinite could help to check the boundedness and convergence of the series considered and then if the integral converged to a finite value, the sum with the expression {(log(f(n)))^(1/n^3)} from n=1 to infinite could converge? I look for a criterion to study series with logarithmic functions but not the typical log(x) but log elevated at an exponent 1/x^3 I mean a logarithm {log(f(x))} ^ (1/x^3). This f(n) can be a special trigonometric function and inside another special function of another proper essence for the nature of the series.
Thanks
Carlos
Question
Good morning, I have meditated about this matter
Let S1-S2 = C , being C a known transcendental number (irrational one)
and S1 and S2 two series given by sequences an =f(n) and bn = g(n) where it is partially known that S2 converges (as I have added more than 8000 terms of expansion on "n", from n=1 to n=8000 or even 9000) and thus the value converges to a real number for S2. I am interested in determining if S1 must be necessarily convergent even considering 8000 or more terms of expansion of S2, then the S1 should written as
S1 = C + S2. with S1 a convergent result thanks to the sum represented here,
with S2 a convergent series based on numerical evaluation of its partial sums or expansion of 8000 terms without rare jumps or divergence. I do not have yet the possibility to calculate S2 in analytical compact way (it is a special sum) of a not determined value or constant, but numerically converges as described.
I would be interested in the more formal theorems or lemmas to support the relationship S1- S2 = transcendental number (irrational one).
Best wishes,
Carlos
Question
How to write formally within the context of mathematics that: "given two series S1 and S2 and they are subtracted each other coming from a proved identity that is true and the result of this subtraction is a known finite number (real number) (which is valid) the two series S1 and S2 are convergent necessarily because the difference could not be divergent as it would contradict the result of convergence? I need that definition within a pure mathematical scenario ( I am engineer).
" Given S1- S2 = c , if c is a finite and real number, and the expression S1-S2 = c comes from a valid deduction, then, S1 and S2 are both convergent as mandatory."
Best regards
Carlos
Question
I am looking a series or relationship that let me write (cot(x))2 and the Appery constant?
I want to write directly the (cot(x))2 by a series or formula based on the Appery constant zeta(3)
Best regards,
Carlos
Question
Is there any possibility to reduce a given denominator tr/p from a term 1/tr/p of an integral after having applied the Feynman's Integral trick and that this step to lead to the domain of the Fractional Laplace Transform analysis when r/p is watch, for example, in F-r/p (s) , s complex variable. The topic seems to me very interesting because one could think in a kind of "continuation" of fractional Laplace transforms to a more general panorama where one can resolve certain divergent series within the context of regularized sum given by certain integrals. For example, if one needs to solve an integral that leads to understand a Laplace definition where the denominator can be "eliminated" conveniently and to compute a function involving a particular series.
Can we speak about Fractional Feynman Trick on Laplace transforms or other contexts?
Thanks
Question
Is there another meaning when "u" is imaginary in some context of physics?
Some general theory for that case.
Thanks in advance
Carlos
Question
The polylogarithm can be expressed in terms of the integral of the Bose–Einstein distribution according to https://en.wikipedia.org/wiki/Polylogarithm
This converges for Re(s) > 0 and all z except for z real and ≥ 1.
I am interested in to know if the same name "the integral of the Bose–Einstein distribution" is still valid for recognizing that integral when z = exp(2*k*i), being i the imaginary unit and k a non-negative integer (k=1, 2, 3...)?
Is that definition for the "integral of the Bose–Einstein distribution" when z=exp(2*k*i) possible or has to be only when z has another domain?
Best regards,
Carlos López
Question
The topic can be complex, but I am interested in the technique of heat kernel for the regularization of a divergent series at a specific point b=0. I mean, if one already knew a convergent series for each point b (being b different to zero where the series diverges), can I transform the divergent series at b=0 in a convergent series at b=0 by the heat kernel regularization or another technique to try to approach the series at the divergent point b=0? I see only the heat kernel or zeta function regularization as potential candidates for fixing divergent series when a specific value b is studied.
Let me know PDFs or links about the regularization from convergent series that diverges at b=0. Particularly I am interested in what has been exposed in this link: https://math.stackexchange.com/questions/1964838/equivalence-of-regularization-schemes-of-divergent-series/4597704#4597704
As the approach seems to be very interesting.
Best regards
Carlos L.
Question
Dear Professors.
I am very interested in sophisticate formulas involving the sum of several Li-functions in infinites terms, like C1*Li(1) + C2*Li(2)+... or others involving the polylogarithm in multiples relationships in infinite sums.
Thanks in advance!
Carlos López
Question
Which are the implications in mathematics if the Irrationality Measure bound of "Pi" is proved to be Less than or equal to 2.5?
How can be understood the number pi within this context?
Thanks,
Carlos

Network

Cited By
    • Xi'an University of Architecture and Technology

Projects

Projects (2)
Project
My goal is to prove the convergence of the Flint-Hills series (and the Cookson's, a parallel series that no-body knows if converges... - Other goal: to set the new specific bound of the irrationality measure of pi, it is 'less than or equal to 2.5' thanks to the proof of the convergence of the Flint-Hills series.
Project
In this project is inferred a set of consequences (new formulas for the Euler-Mascheroni constant, Bernoulli numbers and others) derived from the acceptance of the Riemann Hypothesis (i.e., the non-trivial zeros of the Riemann zeta function have only real part 1/2) and the validity of the property named as 'Hyperbolicity' of Jensen polynomials linked to a particular Taylor series for the Riemann Xi function at the point s=1/2 + i.t.