Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

    Austrian Science Fund (FWF): W1230

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

Project 13:
Additive and combinatorial number theory

Publications 2018

[16] Christian Elsholtz, Jan-Christoph Schlage-Puchta, On Romanov's constant, Mathematische Zeitschrift, (2018). (to appear)
[bib] [doi/article]
[15] Christian Elsholtz, Stefan Planitzer, The number of solutions of the Erd\H os-Straus equation and sums of $k$ unit fractions, (2018). (submitted)
[bib] [arXiv]
[14] Christian Elsholtz, Florian Luca, Stefan Planitzer, Romanov type problems, The Ramanujan Journal, (2018). (to appear)
[bib] [doi/article]

Publications 2017

[13] Rainer Dietmann, Christian Elsholtz, Igor E. Shparlinski, Prescribing the binary digits of squarefree numbers and quadratic residues, Trans. Amer. Math. Soc., 369, 8369-8388, (2017).
[bib] [arXiv] [MR] [doi/article]
[12] Number theory---Diophantine problems, uniform distribution and applications, (Christian Elsholtz, Peter Grabner, eds.), Springer, xv+444, (2017). (Festschrift in honour of Robert F. Tichy's 60th birthday)
[bib] [MR] [doi/article]
[11] Christian Elsholtz, Niclas Technau, Robert Tichy, On the regularity of primes in arithmetic progressions, Int. J. Number Theory, 13(5), 1349—1361, (2017).
[bib] [MR] [doi/article]
[10] Christian Elsholtz, Stefan Planitzer, On Erd\H os and Sárközy's sequences with Property P, Monatsh. Math., 182(3), 565—575, (2017).
[bib] [MR] [doi/article]

Publications 2015

[9] Manfred Madritsch, Stefan Planitzer, Romanov's Theorem in Number Fields, (2015). (preprint)
[bib] [arXiv]
[8] Christian Elsholtz, Adam J. Harper, Additive decompositions of sets with restricted prime factors, Trans. Amer. Math. Soc., 367(10), 7403—7427, (2015).
[bib] [arXiv] [MR] [doi/article]
[7] Rainer Dietmann, Christian Elsholtz, Hilbert cubes in arithmetic sets, Rev. Mat. Iberoam., 31(4), 1477—1498, (2015).
[bib] [arXiv] [MR] [doi/article]
[6] Christian Elsholtz, Glyn Harman, On conjectures of T. Ordowski and Z. W. Sun concerning primes and quadratic forms, Chapter in Analytic number theory (C. Pomerance, M. Rassias, eds.), Springer, 65—81, (2015).
[bib] [MR] [doi/article]

Publications 2014

[5] Christian Elsholtz, Alan Filipin, Yasutsugu Fujita, On Diophantine quintuples and $D(-1)$-quadruples, Monatshefte für Mathematik, 175, 227-239, (2014).
[bib] [MR] [doi/article]

Publications 2013

[4] Andrej Dujella, Christian Elsholtz, Sumsets being squares, Acta Mathematica Hungarica, 141(4), 353-357, (2013).
[bib] [MR] [doi/article]
[3] Rainer Dietmann, Christian Elsholtz, Igor E. Shparlinski, On gaps between primitive roots in the Hamming metric., Quarterly Journal of Mathematics, 64(4), 1043—1055, (2013).
[bib] [arXiv] [MR] [doi/article]
[2] Christian Elsholtz, Clemens Heuberger, Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013).
[bib] [arXiv] [MR] [doi/article]

Publications 2012

[1] Rainer Dietmann, Christian Elsholtz, Hilbert cubes in progression-free sets and in the set of squares, Israel Journal of Mathematics, 192(1), 59-66, (2012).
[bib] [MR] [doi/article]