ARTÍCULOS DE INVESTIGACIÓN
Preprints
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| Quasi Sidon sets |
| Infinite C4-free graphs |
Papers
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| Visible lattice points in random walks (with J.L. Fernández and P. Fernández) European J. Combin. 75 (2019), 92–112. |
| Every positive integer is a sum of three palindromes (with F. Luca and L. Baxter) Math. Comp. 87 (2018), no. 314, 3023–3055. |
| On sets free of sumsets with summands of prescribed size (with R. Tesoro) Combinatorica 38 (2018), no. 3, 511–546. |
| A greedy algorithm for B_h[g] sequences J. Combin. Theory Ser. A 150 (2017), 323–327. |
| Elementary methods for incidence problems in finite fields (with A. Iosevich, B. Lund, O. Roche-Newton and M. Rudnev) Acta Arith. 177 (2017), no. 2, 133–142. |
| Visible lattice points and the chromatic zeta function of a graph Acta Math. Hungar. 151 (2017), no. 1, 1–7. |
| Gaps in sumsets of s pseudo s-th power sequences (with J-M. Deshouillers) Ann. Inst. Fourier (Grenoble) 67 (2017), no. 4, 1725–1738. |
| Ratio sets of random sets (with J. Guijarro) The Ramanujan Journal 43 (2017), no. 2, 327–345. |
| Saving the logarithm factor in the error term estimates of some congruences problems (with A. Zumalacárregui) Math. Z. 286 (2017), no. 1-2, 545–558. |
| Additive properties of sequences of pseudo s-th powers (with J-M. Deshouillers, V. Lambert and A. Plagne) Math. Zeitschrift 284 (2016), no. 1-2, 175–193. |
| On product sets of rationals International Journal of Number Theory 12 (2016), no. 5, 1415–1420.. |
The congruence x^x= lambda (mod p) (with M. Garaev) Proc. Amer. Math. Soc., vol 144, nº 6 (2016)
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| Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications (with M. Garaev) Mathematical Proceedings Cambridge Philosophical Society
, vol 160, nº 3 (2016) |
| Carmichael numbers in the sequence k·2^n+1 (with F. Luca and A. Pizarro) Mathematics of Computation, vol 85, nº 297 (2016) |
| On Sidon sets and asymptotic bases Proceedings of the London Mathematical Society, vol 111, nº5 (2015) |
| Dense infinite Bh sequences (with R. Tesoro) Publicacions Matematiques, vol 59, nº1 (2015) |
| k-fold Sidon sets (with C. Timmons) Electronic Journal of Combinatorics vol 21, nº4 (2014) |
| Points on curves in small boxes and applications (with M.-C. Chang, M. Garaev, J. Hernández, I. Shparlinski and A. Zumalacárregui) Michigan Mathematical Journal, vol 63, nº3 (2014) |
| A note on distinct distances in rectagular lattice (with M. Sharir and A. Sheffer) Discrete Mathematics, vol 93 (2014) |
| The least common multiple of random sets of positive integers (with J. Rué, P. Sarka and A. Zumalacárregui), Journal of Number Theory vol 144 (2014) |
| An additive problem in finite fields of powers of elements of large multiplicative order (with A.Zumalacárregui) Revista Matemática Complutense, vol 27, nº 2 (2014) |
| 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)
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| 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)
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B2[g] sets and a conjecture of Schinzel and Schmidt (with C. Vinuesa) Combinatorics, Probability and Computing, vol 17, nº6 (2008)
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Squares in (1^2+1).....(n^2+1) Journal of Number Theory, vol
128, nº8 (2008)
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| 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)
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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)
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An Overlapping theorem with applications (with G. Tenenbaum) Publicacions matematiques, nº 1 (2007)
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Real and p-adic Sidon sequences (with I.Ruzsa) Acta Sci. Math. (Szegez) vol 70, nº 3-4 (2004)
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Lattice points on circles Journal Australian Mathematical Sociecty, vol 72, nº 2 (2002)
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Upper and lower bounds for
finite Bh[g] sequences (with I. Ruzsa and C. Trujillo) Journal of Number Theory, vol 97, nº1 (2002)
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New upper bounds for Bh sequences Advances in Mathematics, vol 159, nº1 (2001)
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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)
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Infinite B2[g] sequences (with C. Trujillo) Israel Journal of Mathematics, vol 126 (2001)
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| 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)
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The
Hyperbola xy=N (with J. Jimenez) Journal of Théorie des
Nombres of Bordeaux, vol 12, nº 1 (2000)
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An upper bound for B2[2] sequences Journal of Combinatorial
Theory Ser. A vol 89, nº 1 (2000)
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Gaps in dense Sidon sets Integers: the electronic Journal of
Combinatorial Number Theory, vol 0 A11 (2000)
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Divisors in a Dedekind domain (with J. Jiménez) Acta Aritmetica, vol 85, nº 3 (1998)
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Lattice points on hyperbolas (with
J. Jiménez) Jourmal of Number Theory, vol 63 , nº 2 (1997)
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B2[g] sequences whose terms are squares Acta Mathematica Hungarica, vol 67, nº 1-2 (1995)
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Lattice points on ellipses (with A. Córdoba) Duke Mathematical Journal, vol 76, nº 3 (1994)
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The distribution of the lattice
points on circles Journal of Number Theory, vol 43, nº 2 (1993)
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The additive complection of k-powers Journal of Number Theory, vol 44, nº 3 (1993)
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B2[infty]-sequences of square
numbers (with A. Córdoba) Acta Arithmetica, vol 61, nº 3 (1992)
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Trigonometric polynomials and
lattice points (with A. Córdoba) Proc. Amer. Math. Soc. vol 115, nº 1 (1992)
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Arcs containing no three lattice
points Acta Arithmetica, vol 59, nº 1 (1991)
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| B2 sequences whose terms are
squares Acta Arithmetica, vol 55, nº 3 (1990) |
LIBROS y edicción de ACTAS |
| Conjuntos de Sidon Escuela Venezolana de Matemáticas (2014) |
| ¿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) |