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

[25]C. Elsholtz and S. Planitzer, Sums of four and more unit fractions and approximate parametrizations, Bulletin of the London Mathematical Society, 53(3), 695-709. [bibtex] [doi]
2012
[24]Rainer Dietmann and Christian Elsholtz, Hilbert cubes in progression-free sets and in the set of squares, Israel Journal of Mathematics, 192(1), 59-66, (2012). [bibtex] [doi]
2013
[23]Christian Elsholtz, Clemens Heuberger and Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013). [bibtex] [doi]
[22]Rainer Dietmann, Christian Elsholtz and Igor E. Shparlinski, On gaps between primitive roots in the Hamming metric., Quarterly Journal of Mathematics, 64(4), 1043–1055, (2013). [bibtex] [doi]
[21]Andrej Dujella and Christian Elsholtz, Sumsets being squares, Acta Mathematica Hungarica, 141(4), 353-357, (2013). [bibtex] [pdf] [doi]
2014
[20]Christian Elsholtz, Alan Filipin and Yasutsugu Fujita, On Diophantine quintuples and $D(-1)$-quadruples, Monatshefte für Mathematik, 175, 227-239, (2014). [bibtex] [pdf] [doi]
2015
[19]Elsholtz, Christian and Harman, Glyn, 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). [bibtex] [doi]
[18]Dietmann, Rainer and Elsholtz, Christian, Hilbert cubes in arithmetic sets, Rev. Mat. Iberoam., 31(4), 1477–1498, (2015). [bibtex] [doi]
[17]Elsholtz, Christian and Harper, Adam J., Additive decompositions of sets with restricted prime factors, Trans. Amer. Math. Soc., 367(10), 7403–7427, (2015). [bibtex] [doi]
[16]Madritsch, Manfred and Planitzer, Stefan, Romanov's Theorem in Number Fields, (2015). (preprint) [bibtex]
2017
[15]Elsholtz, Christian and Planitzer, Stefan, On Erd\H os and Sárközy's sequences with Property P, Monatsh. Math., 182(3), 565–575, (2017). [bibtex] [doi]
[14]Elsholtz, Christian, Technau, Niclas and Tichy, Robert, On the regularity of primes in arithmetic progressions, Int. J. Number Theory, 13(5), 1349–1361, (2017). [bibtex] [doi]
[13]Number theory—Diophantine problems, uniform distribution and applications, (Elsholtz, Christian, Grabner, Peter, eds.), Springer, xv+444, (2017). (Festschrift in honour of Robert F. Tichy's 60th birthday) [bibtex] [doi]
[12]Dietmann, Rainer, Elsholtz, Christian and Shparlinski, Igor E., Prescribing the binary digits of squarefree numbers and quadratic residues, Trans. Amer. Math. Soc., 369, 8369-8388, (2017). [bibtex] [doi]
2018
[11]Elsholtz, Christian and Schlage-Puchta, Jan-Christoph, On Romanov's constant, Math. Z., 288(3-4), 713–724, (2018). [bibtex] [url] [doi]
[10]Elsholtz, Christian, Luca, Florian and Planitzer, Stefan, Romanov type problems, Ramanujan J., 47(2), 267–289, (2018). [bibtex] [url] [doi]
[9]Stefan Planitzer, Sums of unit fractions, Romanov type problems and Sequences with Property P, PhD thesis, TU Graz, (2018). [bibtex]
2019
[8]Elsholtz, Christian and Frei, Christopher, Arithmetic progressions in binary quadratic forms and norm forms, Bull. Lond. Math. Soc., 51(4), 595–602, (2019). [bibtex] [url] [doi]
2020
[7]Elsholtz, Christian and Schlage-Puchta, Jan-Christoph, The density of integers representable as the sum of four prime cubes, Acta Arith., 192(4), 363–369, (2020). [bibtex] [url] [doi]
[6]Elsholtz, Christian and Planitzer, Stefan, The number of solutions of the Erd\Hos-Straus equation and sums of $k$ unit fractions, Proc. Roy. Soc. Edinburgh Sect. A, 150(3), 1401–1427, (2020). [bibtex] [url] [doi]
[5]Elsholtz, Christian, Unconditional Prime-Representing Functions, Following Mills, Amer. Math. Monthly, 127(7), 639–642, (2020). [bibtex] [url] [doi]
[4]Elsholtz, Christian and Pach, Péter Pál, Caps and progression-free sets in $\mathbb{Z}^n_m$, Designs, Codes and Cryptography, 88(10), 1–38, (2020). [bibtex] [doi]
[3]B. Klahn, A divisor problem for polynomials, (2020). (submitted) [bibtex]
[2]C. Elsholtz and G. Lipnik, Exponentially larger affine and projective caps, (2020). (submitted) [bibtex]
2021
[1]Christian Elsholtz, Fermat’s Last Theorem Implies Euclid’s Infinitude of Primes, The American Mathematical Monthly, 128(3), 250-257, (2021). [bibtex] [doi]