Memorial to Javier Cilleruelo: a problem list. (English) Zbl 1412.11055

Summary: This is a list of problems in combinatorial number theory gathered on the occasion of the meeting “The Music of Numbers” to honor the memory of the late Javier Cilleruelo (1961 – 2016).


11B75 Other combinatorial number theory
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Cilleruelo, Javier
Full Text: Link


[1] P. Cameron, J. Cilleruelo and O. Serra, On monochromatic solutions of equations in groups, Rev. Mat. Iberoam. 23 (2007), 385-395. · Zbl 1124.05086
[2] J. Cilleruelo, The least common multiple of a quadratic sequence, Compos. Math. 147 (2011), 1129-1150. · Zbl 1248.11068
[3] J. Cilleruelo and J-M. Deshouillers, Gaps in sumsets of s pseudo s-th power sequences, Ann. Inst. Fourier (Grenoble) 67 (2017), 1725-1738. · Zbl 1433.11005
[4] J. Cilleruelo, J-M. Deshouillers, V. Lambert, and A. Plagne, Additive properties of pseudo s-th power sequences, Math. Z. 284 (2016), 175-193. · Zbl 1393.11025
[5] J. Cilleruelo and M. Z. Garaev, Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications, Math. Proc. Cambridge Philos. Soc. 160 (2016), no. 3, 477-494. · Zbl 1371.11003
[6] J. Cilleruelo, F. Luca, and L. Baxter, Every positive integer is a sum of three palindromes, Math. Comp., published electronically (2017), https://doi.org/10.1090/mcom/3221. · Zbl 1441.11016
[7] J. Cilleruelo, D.S. Ramana, and O. Ramar´e, Quotients and product sets of thin subsets of the positive integers, Proc. Steklov Inst. Math. 296 (2017), 52-64. · Zbl 1371.11023
[8] J. Cilleruelo, J. Ru´e, P. Sarka, and A. Zumalac´arregui, The least common multiple of random sets of positive integers, J. Number Theory 144 (2014), 92-104. · Zbl 1296.11007
[9] A. C´ordoba, E. Latorre, Radial multipliers and restriction to surfaces of the Fourier transform in mixed-norm spaces, Math. Z. 286 (2017), 1479-1493. · Zbl 1376.42013
[10] J-M. Deshouillers, F. Hennecart, and B. Landreau, Sums of powers: an arithmetic refinement to the probabilistic model of Erd˝os and R´enyi, Acta Arith. 85 (1998), 13-33.
[11] J-M. Deshouillers, F. Hennecart, and B. Landreau, Do sums of 4 biquadrates have a positive density?, Algorithmic number theory, 196-203, Lecture Notes in Comput. Sci. 1423, Springer, Berlin, 1998.
[12] J-M. Deshouillers, F. Hennecart, and B. Landreau, On the density of sums of three cubes, Algorithmic number theory, 141-155, Lecture Notes in Comput. Sci. 4076, Springer, Berlin, 2006. · Zbl 1143.11347
[13] J-M. Deshouillers and M. Iosifescu, Sommes de s + 1 pseudo-puissances s-i‘emes, Rev. Roumaine Math. Pures Appl. 45 (2000), 427-435. · Zbl 0987.11060
[14] W. Duke, J. Friedlander, and H. Iwaniec, Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. (2) 141 (1995), no. 2, 423-441. · Zbl 0840.11003
[15] P. Erd˝os and A. R´enyi, Additive properties of random sequences of positive integers, Acta Arith. 6 (1960), 83-110.
[16] K. Homma, On the discrepancy of uniformly distributed roots, J. Number Theory 128 (2008), 500-508. · Zbl 1195.11089
[17] P. A. Parrilo, A. Robertson, and D. Saracino, On the asymptotic minimum number of monochromatic 3-term arithmetic progressions, J. Combin. Theory Ser. A 115 (2008), 185192. · Zbl 1210.05172
[18] J. Ru´e, P. Sarka, A. Zumalac´arregui, On the error term of the logarithm of the lcm of quadratic sequences, J. Th´eor. Nombres Bordeaux 25 (2) (2013) 457-470.
[19] ´A. T´oth, Roots of quadratic congruences, Internat. Math. Res. Notices 2000, no. 14, 719-739. · Zbl 1134.11339
[20] J. Wolf, The minimal number of monochromatic 4-term progressions inZp, J. Comb. 1 (2010), 53-68. · Zbl 1227.11037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.