Sorry for my English in this page. I know that it is very bad, and I'm sure that a lot of grammar and spelling corrections should be added.

Welcome to the Juan L. Varona WWW page. It offers information about myself, as well as on aspects related to my research and subjects of personal interest. Also, pushing here you can get many of my research papers and other publications. If, instead, you are interested in my teaching at the university, push here. And here you have my complete address. Recently, I have written a book devoted to the Theory of Numbers (second edition published on 2019). You can get more information in this page (in Spanish). Moreover, I am Editor-in-Chief of La Gaceta de la Real Sociedad Matemática Española and I have been President of CervanTeX (the Spanish speakers TeX Users Group) for ten years. |

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Papers |
Seminario |
Aliquot sequences |
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TeX/LaTeX |
Spanish keyboard for TeX in Mac |

- Fourier series of orthogonal polynomials, both classic polynomials and modifications of the measurement adding deltas of Dirac.
- Fourier-Bessel Series.
- Series of Neumann type, and its relation with Hankel transform and the dual integral equations.
- Fourier series related to the Dunkl transform, as well as sampling theorems and uncertainty.

On the other hand, years ago, I developed several applications for Macintosh that allow to draw fractals or drawings coming from dynamic systems. But for a long time I have not been updating them; as a consequence, they are not Power Macintosh native and they seem poor if compared with more modern others. Someday I will retake this.

If a positive integer number n is taken, we denote
sigma(n) the sum of its divisors (including 1 and n), and s(n) =
sigma(n)-n the sum of its divisors without n. By iterating the function,
it appears the so called aliquot sequence. For instance, n = 20,
s(20) = 1+2+4+5+10 = 22, s(22) = 1+2+11 = 14, s(14) = 1+2+7 =
10, s(10) =... Then, the conjecture of Catalan-Dickson assures that
all these sequences finish in 1 (being the previous term a prime number),
a perfect number, a pair of amicable numbers, or a cycle. No counterexample is
known nor the conjecture is proved. In this subject I have worked in
collaboration with Manuel Benito
(who, by the way, also has written
a book on Brocot sequences).
We have obtained **a computation record**: The
aliquot sequence that begins in 3630 converges to 1 in 2624
iterations after to have reached a maximum of 100 digits (in base 10)
in iteration 1263.

If you are interested in this, click here to find more information on our work (in English). In Spanish, you can read this article, that is an enlargement of the one that appeared published in La Gaceta de la RSME. Also you can accede directly from here to the table with the present state of the sequences that begin in a number smaller than 10000 and whose end is (still) not known, and to the tables of 80 digits, 90 digits and 100 digits.

Now, my research work related to number theory is not so divulgative, and can be found in the page with my publications.

The Department of Mathematics and Computation of the University of La Rioja has published a book in honour of him (for historial interest, this is of the page with the call). The publishers of the book have been Luis Español and myself.

For more info, and for download it, push here (in Spanish).

For more info, push here (in Spanish).

For more info, and to see the complete list of talks since it began in 1978, push here (in Spanish).

The digital journal Matematicalia has published an article (in Spanish) about our Seminario Permanente, the oldest divulgative mathematical seminary in Spain. You can also download it in pdf, tex or self-contained web page.

Together with M. Sanz-Solé, J. Soria and J. Verdera,
I were editor of
*Proceedings of the International Congress of Mathematicians*,
European Mathematical Society Publishing House, 2006 (Vol. II and III)
and 2007 (Vol. I).

LaTeX es a more powerful and easy of use language; it is based on TeX.

I have collaborated in the activities of the Spanishspeaking TeX User Group, a.k.a. CervanTeX, of whom I am a member. Time ago, I participated actively in the writing of its statutes.

I have always been interested in the developments of TeX to write in Spanish. I have collaborated making dictionaries, keyboard layouts, packages, collecting utilities and information, etc. Also, I support the server ftp://tex.unirioja.es/pub/tex, where you can found many material to download. For more info, push here (in Spanish).

If you are looking how to use TeX/LaTeX in a Macintosh computer (and how to install it), read the next item.

With Mac OS X, I recommend you the following material related with TeX (everything is free and can be downloaded in the corresponding links; but read up to the end of this section before to install):

- The front-end, i.e., the user interface to write the .tex file in it,
to use the typeset button, to print, ...:
TeXShop,
by Richard Koch and the help of many people.
In particular, I make the localization in Spanish.
Important:
**TeXShop is not useful without installing TeX Live**(see in the in the next item). - The kernel (TeX itself): TeX Live, that has been developed by collaboration between many TeX users groups in the world. (teTeX and the i-Installer, from Gerven Wierda, is now obsolete).
- A spell checker (i.e., a dictionary) based on aspell: CocoAspell, by Anton Leuski. It acts as a service of Mac OS X and can be used not only with TeXShop, but by any other Cocoa application. I also made the localization into Spanish.
- Another spell checker: Excalibur, by Rick Zaccone. I wrote the Spanish dictionary (it has 292 thousand words).

Finally, it will perhaps be usefull for you a **keyboard layout developed by myself**; it is particularly well adapted to write
TeX/LaTeX in a Mac with a Spanish keyboard.
Push here to read more information,
or download it;
it includes a file "Readme" with instruccions of how to use and how to install it. Check it!

As a general rule, *software should be free.*
There exists free software of a great quality (adn, moreover, there are
awful comercial software).
In particular, I advocate you for using free software when possible.
There are powerful reasons that can incite you:

- It is economically profitable, and you contribute to avoid that some people to enrich with your money.
- If you collaborate with the developers, you can help to improve the product.
- You will avoid the problems of proprietary and close formats.
- You will contribute to a more free world.
- You will enjoy with all of this.

For mathematics, I suggest you try Sage,
whose target is "*Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab*".

When I noticed the error, I take the initiative in get the change from "Alfarense" to "Alfareño". After contact with the RAE (actually, with its Instituto de Lexicografía) and realize a lot of efforts, some of them with the help of the Ayuntamiento de Alfaro, I had success. In the edition 22 (year 2001) of the Diccionario of the RAE already appears "Alfareño" (and "Alfarense" has been removed).

I cannot finish without advocate you for visiting
Alfaro.
It is an eminently agricultural village with about 10 thousand people.
But it is internationally known because it has
the biggest urban colony of storks in the world,
a big part of it in the roofs of
San Miguel's Church.
It is marvelous to observe them from the balcony. |

- The Real Sociedad Matemática Española (RSME), and Editor-in-Chief of La Gaceta de la RSME.
- The Sociedad Española de Matemática Aplicada (SEMA).
- The Sociedad Riojana de Profesores de Matemáticas (A prima).
- The American Mathematical Society (AMS).
- Former member of the Comisión de Información y Comunicación Electrónicas of the Comité Español de Matemáticas (CEMAT).
- The Grupo de Usuarios de TeX Hispanohablantes CervanTeX (president between May 2005 and February 2016).
- The TeX Users Group TUG.
- The Agrupación Astronómica de La Rioja (AAR).
- The Community of Neighbors of my house (web page under construction).

Juan Luis Varona

Dpto. de
Matemáticas y Computación

Universidad de La Rioja

Complejo Científico-Tecnológico

Calle Madre de Dios 53

26006 Logroño, Spain

**Tel.**: 34 - 941 299 451. **Fax**: 34 - 941 299 460

*Last modification of
this page:
February 21, 2019*