PÁGINA PRINCIPAL



ARTÍCULOS DE INVESTIGACIÓN

Preprints
Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime  (with M. Garaev)
A note on product sets of rationals
Gaps in sumsets of s pseudo s-th power sequences  (with J-M. Deshouillers)
Infinite graphs that do not contain cycles of length four
Saving the logarithm factor in the error term estimates of some congruences problems  (with A. Zumalacárregui) 
k-fold Sidon sets (with C. Timmons)
Sidon basis 
On lattices, distinct distances and the Elekes-Sharir framework (with M. Sharir and A. Sheffer)
Carmichael numbers in the sequence k·2^n+1 (with  F. Luca and A. Pizarro)
The least common multiple of sets of positive integers (with  J. Rué, P. Sarka and A. Zumalacárregui)

Papers

Concentration of points and isomorphism classes of hyperelliptic curves over a finite field in some thin families  (with M.-C. Chang, M. Garaev, J. Hernández, I. Shparlinski and A. Zumalacárregui)    Michigan Mathematical Journal,  (to appear)
Dense infinite Bh sequences (with R. Tesoro)  Publicacions Matematiques,  (to appear)
An additive problem in finite fields of powers of elements of large multiplicative order (with A.Zumalacárregui)  Revista Matemática Complutense, (to appear)
Infinite Sidon sequences  Advances in Mathematics,  vol 255 (2014) 
Palindromes in linear recurrence sequences  (with F. Luca and R. Tesoro)  Monatshefte für Mathematik, vol 171, nº 3-4  (2013)
Concentration of points on curves in finite fields  (with I. Shparlinski)  Monatshefte für Mathematik, vol 171, nº 3-4  (2013)
Dense sets of integers with prescribed representation function   (with M. Nathanson)  European Journal of Combinatorics, vol 34, nº 8, 1297-1306 (2013)
On the fractional parts of a^n/n  (with A. Kumchev, F. Luca, J. Rué and I. Shparlinski)  Bull. of the London Math. Soc.  vol 45, nº 2, 249-256 (2013)
On the sums of digits of the some sequences of integers (with F. Luca, J. Rué and A. Zumalacárregui) Central European Journal of Mathematics vol 11, nº 1  (2013)
Combinatorial problems in finite fields and Sidon sets  Combinatorica  vol 32, nº 5  (2012)
On the largest prime factor of the partition function of n  (with F. Luca)  Acta Arithmetica  vol 156, nº 1  (2012)
On the concentration of points of polynomial maps and applications  (with M. Garaev, A. Ostafe and I. Shparlinski)  Math. Zeitschrift, vol 272, nº 3-4  (2012)
Isomorphism classes of elliptic curves over a finite field in some thin families  (with I. Shparlinski and A. Zumalacárregui)  Math. Research Letters, vol 19,  nº 02  (2012)
Concentration of points on two and three dimensional modular hyperbolas and applications  (with M. Garaev)  Geometric and Functional Analysis,  vol 21 , nº4  (2011)  
The least common multiple of a quadratic sequence   Compositio Mathematica,  vol 147, nº4 (2011) 
Repunit Lehmer numbers  (with  F. Luca)  Proceedings of the Edinburgh Mathematical Society,  vol 54, nº1 (2011)
Generalization of a theorem of Erdos and Renyi on Sidon sets  (with S. Kiss, I. Ruzsa and C. Vinuesa)  Random Structures and Algorithms,  vol 37, nº4 (2010)
On a question of Sarkozy on gaps of product sequences   (with Thai Hoang Le)  Israel Journal of Mathematics,  vol 179, (2010)
Generalized Sidon sets  (with I. Ruzsa and C. Vinuesa)  Advances in Mathematics  vol 225, nº5  (2010)
Fibonacci lattice points  (with  F. Luca)  The Ramanujan Journal   vol 22,  nº3 (2010)
Probabilistic constructions of B2[g] sequences    Acta Mathematica Sinica   vol 26,  nº7 (2010)
The number of rational numbers determined by large sets of integers  (with S. Ramana and O. Ramaré)  Bull. of the London Math. Soc.  vol 42,  nº3 (2010)
Sidon sets in N^d    Journal of Combinatorial Theory Ser. A  vol 117,  nº7 (2010)
Addition theorems in acyclic semigroups  (with  Y.Hamidoune and O. Serra)  Additive Number Theory: Festschrift in Honor of the Sixtieth Birthday of Melvyn B. Nathanson. Springer Verlag,  May (2010)
A sumset problem  (with M. Silva and C. Vinuesa)   Journal of Combinatorics and Number Theory  vol 2,  nº1 (2010)
On multiplicative magic squares (with  F. Luca)  The Electronic Journal of Combinatorics  vol 17,  nº2 (2010)
On Squares in polynomial products    (with F. Luca, A. Quirós and I. Shparlinski)   Monatshefte für Mathematik, vol 159, nº3 (2010)
Close lattice points on circles  (with A. Granville)   Canadian Journal of Mathematics,  vol 61, nº6 (2009)
Powers values of palindromes  (with F. Luca and I. Shparlinski)   Journal of Combinatorics and Number Theory, vol 1, nº2  (2009)
On sums of dilates  (with Y. Hamidoune and O. Serra)   Combinatorics, Probability and Computing,  vol 18, nº6  (2009)
Discrepancy in generalized arithmetic progressions  (with N. Hebbinghaus)   European Journal of Combinatorics, vol 30  (2009)
Least totients in arithmetic progressions    (with  M. Garaev)   Proceedings of the American Mathematical Society, vol 137  (2009)
On a question on Sarkozy and Sos for bilinear forms  (with J. Rué)   Bulletin of the London Mathematical Society,  vol 41,  nº2  (2009)  
On the sum of the first n primes  (with F. Luca)  The Quarterly Journal of Mathematics,   vol 59, nº4   (2008)
Perfect difference sets constructed from Sidon sets   (with M. Nathanson)  Combinatorica,     vol 28, nº4  (2008)
B2[g] sets and a conjecture of Schinzel and Schmidt  (with C. Vinuesa)  Combinatorics, Probability and Computing,   vol 17, nº6  (2008)
Squares in (1^2+1).....(n^2+1)  Journal of Number Theory,   vol 128, nº8  (2008)
Conjuntos de Sidon bidimensionales y aplicaciones  Actas de las VI Jornadas de Matemática Discreta y Algorítmica,   (2008)
On Monochromatic solutions of equations in groups  (with  P. Cameron and O. Serra)  Revista Matemática Iberoamericana,    vol 23, nº1  (2007)
Lattice points on circles, squares in arithmetic progressions and sumsets of squares  (with A. Granville) in "Additive Combinatorics",  CRM Proceedings & Lecture Notes,  RI, Amer. Math. Soc.   vol 43  (2007)
An Overlapping theorem with applications (with G. Tenenbaum)  Publicacions matematiques,   nº 1  (2007)
Real and p-adic Sidon sequences (with I.Ruzsa)  Acta Sci. Math. (Szegez)  vol 70, nº 3-4  (2004)
Lattice points on circles  Journal Australian Mathematical Sociecty,  vol 72, nº 2   (2002)
Upper and lower bounds for finite Bh[g] sequences (with I. Ruzsa and C. Trujillo)  Journal of Number Theory,  vol 97, nº1  (2002)
New upper bounds for Bh sequences  Advances in Mathematics,  vol 159, nº1  (2001)
The Severi bound on sections of rank two semistable bundles on a Riemann surface  (with I. Sols)  Annals of Mathematics,  vol 154, nº 3   (2001)
Infinite B2[g] sequences (with C. Trujillo)  Israel Journal of Mathematics,  vol 126   (2001)
Squares with four equal digits in an even base (solution to the problem 10741)   American Mathematical Monthly,  vol 108,  nº3  (2001)
Bh[g] sequences  (with J. Jiménez)  Mathematika,  vol 47, nº1-2  (2000)
The Hyperbola xy=N (with J. Jimenez)  Journal of Théorie des Nombres of  Bordeaux,   vol 12, nº 1 (2000) 
An upper bound for B2[2] sequences  Journal of Combinatorial Theory Ser. A   vol 89, nº 1 (2000)
Gaps in dense Sidon sets  Integers: the electronic Journal of Combinatorial Number Theory,   vol 0 A11 (2000)
Divisors in a Dedekind domain  (with J. Jiménez)  Acta Aritmetica,    vol 85, nº 3   (1998)
Lattice points on hyperbolas (with J. Jiménez)  Jourmal of Number Theory,  vol 63 , nº 2   (1997)
B2[g] sequences whose terms are squares   Acta Mathematica Hungarica,   vol 67, nº 1-2   (1995)
Lattice points on ellipses (with A. Córdoba)  Duke Mathematical Journal,  vol 76, nº 3   (1994)
The distribution of the lattice points on circles  Journal of  Number Theory,   vol 43, nº 2   (1993)
The additive complection of k-powers  Journal of  Number Theory,   vol 44, nº 3   (1993)
B2[infty]-sequences of square numbers (with A. Córdoba)  Acta Arithmetica,   vol 61, nº 3   (1992)
Trigonometric polynomials and lattice points   (with A. Córdoba)  Proc. Amer. Math. Soc.  vol 115, nº 1    (1992)
Arcs containing no three lattice points  Acta Arithmetica,   vol  59, nº 1     (1991)
B2 sequences whose terms are squares  Acta Arithmetica,   vol  55, nº 3    (1990)


LIBROS y edicción de ACTAS
¿Qué sabemos de...? Los números. (con A.Córdoba)  Editorial Catarata (2010)
Combinatorial Number Theory and Additive Group Theory. Coordinador (con O. Serra) Autores: A. Geroldinger and I. Ruzsa. Advanced Courses in Mathematics - CRM Barcelona . Birkhausser (2009)
Proceedings of the Segundas Jornadas de Teoría de Números. Editor ( con E. González, A. Quirós y X. Xarles). Colección Biblioteca de la Revista Matemática Iberoamericana (2008)
La Teoría de los Números. (con A. Córdoba). Editorial Mondadori (1992)


ARTÍCULOS DE DIVULGACIÓN 
Conjuntos con todas las diferencias distintas   Gaceta de la Real Sociedad Matemática Española,  vol 11,  nº1  (2008)
Entrevista con Terence Tao, Medalla Fields en el ICM Madrid 2006  (con A. Quirós y A. Vargas)  Gaceta de la Real Sociedad Matemática Española,  vol 9,  nº3  (2006)
Esquivando cuadrados (solución al problema 38*)  Gaceta de la Real Sociedad Matemática Española,  vol 9,  nº2  (2006)
Cuadrados latinos,   Fotografiando las matemáticas, Edit. Carriogo (2000)
La demostración elemental del teorema del número primo,   Las matemáticas del siglo XX,  Edit. Nivola (2000)
La conjetura de Goldbach,   Gaceta de la Real Sociedad Matemática Española,  vol 3,  nº3  (2000)
El sistema binario,   Gaceta de la Real Sociedad Matemática Española,  vol 2,  nº1  (1999)
Cuadrados Mágicos,   Gaceta de la Real Sociedad Matemática Española,  vol 1,  nº3  (1998)
Progresiones aritméticas en sucesiones de enteros,   Gaceta de la Real Sociedad Matemática Española,  vol 1,  nº2  (1998)
e