Christian Elsholtz

Research output

Research output per year 2001 2012 2013 2015 2016 2017 2020 2023

• 57 Article
• 4 Chapter
• 3 Conference paper
• 1 Anthology

Research output per year

Research output per year

Search results

• 2023

  Exponentially Larger Affine and Projective Caps

  Elsholtz, C. & Lipnik, G. F., Jan 2023, In: Mathematika. 69, 1, p. 232-249 18 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Projective 100%
  • Affine Space 50%

• Large subsets of Z_m^n without arithmetic progressions

  Elsholtz, C., Klahn, B. & Lipnik, G. F., Apr 2023, In: Designs, Codes, and Cryptography. 91, 4, p. 1443-1452 10 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Bounds 100%
  • Arithmetic Progression 100%
  • Integer 33%
  • Prime Factor 33%

• Longer Gaps Between Values of Binary Quadratic Forms

  Dietmann, R., Elsholtz, C., Kalmynin, A., Konyagin, S. & Maynard, J., 1 Jun 2023, In: International Mathematics Research Notices. 2023, 12, p. 10313-10349 37 p.

  Research output: Contribution to journal › Article › peer-review
• 2022

  Egyptian fractions

  Elsholtz, C. & Bloom, T., 2022, In: Nieuw Archief voor Wiskunde. 23, 4, p. 237-245

  Research output: Contribution to journal › Article › peer-review

• On polynomials with roots modulo almost all primes

  Elsholtz, C., Klahn, B. & Technau, M., 2022, In: Acta Arithmetica. 205, 3, p. 251-263 13 p.

  Research output: Contribution to journal › Article › peer-review

  • Polynomial 100%
  • Modulo 100%
  • Roots 100%
  • Integer 75%
  • Finite Number 25%

• Some results of James Maynard

  Elsholtz, C. & Tichy, R., 2022, In: Internationale Mathematische Nachrichten.

  Research output: Contribution to journal › Article
• 2021

  Fermat’s Last Theorem Implies Euclid’s Infinitude of Primes

  Elsholtz, C., 2021, In: American Mathematical Monthly. 128, 3, p. 250-257 8 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Necessary Condition 100%

• Sums of four and more unit fractions and approximate parametrizations

  Elsholtz, C. & Planitzer, S., Jun 2021, In: Bulletin of the London Mathematical Society. 53, 3, p. 695-709 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Number 100%
  • Upper Bound 100%
  • Approximates 100%
  • Unit Fraction 100%
  • Rational Number 66%
• 2020

  Caps and progression-free sets in Zmn

  Elsholtz, C. & Pach, P. P., 1 Oct 2020, In: Designs, Codes, and Cryptography. 88, 10, p. 2133-2170 38 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Progression Free Survival 100%

• The density of integers representable as the sum of four prime cubes

  Elsholtz, C. & Schlage-Puchta, J. C., 1 Jan 2020, In: Acta Arithmetica. 192, 4, p. 363-369 7 p.

  Research output: Contribution to journal › Article › peer-review

  • Cube 100%

• The number of solutions of the Erdos-Straus Equation and sums of k unit fractions

  Elsholtz, C. & Planitzer, S., 2020, In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 150, 3, p. 1401 - 1427

  Research output: Contribution to journal › Article › peer-review

  • Rational Number 100%

• Unconditional Prime-Representing Functions, Following Mills

  Elsholtz, C., 8 Aug 2020, In: The American Mathematical Monthly. 127, 7, p. 639-642 4 p.

  Research output: Contribution to journal › Article › peer-review

  • Prime Number 100%
  • Riemann Hypothesis 100%
• 2019

  Arithmetic progressions in binary quadratic forms and norm forms

  Elsholtz, C. & Frei, C., 2019, In: The Bulletin of the London Mathematical Society. 2019, 51(4), p. 595-602

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Arithmetic Progression 100%
  • Common Difference 50%

• Sums of two numbers having only prime factors congruent to one modulo four

  Elsholtz, C. & Dietmann, R., 2019, Banach Center publications: Number theory week 2017. Warschau, Vol. 118. p. 177-179

  Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

• The maximal order of iterated multiplicative functions

  Elsholtz, C., Technau, M. & Technau, N., 30 Jul 2019, In: Mathematika. 65, 4, p. 990-1009 20 p.

  Research output: Contribution to journal › Article › peer-review
• 2018

  On Romanov's constant

  Elsholtz, C. & Schlage-Puchta, J-C., 2018, In: Mathematische Zeitschrift. 288, p. 713-724

  Research output: Contribution to journal › Article › peer-review

• Romanov type problems

  Elsholtz, C., Luca, F. & Planitzer, S., 2018, In: The Ramanujan Journal. 47, 2, p. 267-289

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Integer 100%
  • Positive Integer 75%
  • Arithmetic Progression 50%
  • Direction 25%
• 2017

  Golomb's conjecture on prime gaps

  Elsholtz, C., 2017, In: The American Mathematical Monthly. 124, 4, p. 365-368

  Research output: Contribution to journal › Article › peer-review

• Local oscillations in moderately dense sequences of primes

  Brüdern, J. & Elsholtz, C., 1 Jun 2017, Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday. Springer International Publishing AG , p. 193-210 18 p.

  Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

  • Quantitative Measure 100%
  • Sharp Estimate 100%

• Maximal sumfree sets of integer lattice grids

  Elsholtz, C. & Rackham, L., 2017, In: Journal of the London Mathematical Society. 95, 2, p. 353-372

  Research output: Contribution to journal › Article › peer-review

• Number Theory – Diophantine Problems, Uniform Distribution and Applications

  Elsholtz, C. & Grabner, P., 2017, Springer International Publishing AG . 444 p.

  Research output: Book/Report › Anthology › peer-review

• On Erdős and Sárközy’s sequences with Property P

  Elsholtz, C. & Planitzer, S., Mar 2017, In: Monatshefte für Mathematik. 182, 3, p. 565–575

  Research output: Contribution to journal › Article › peer-review

  Open Access

• On the regularity of primes in arithmetic progressions

  Elsholtz, C., Technau, N. & Tichy, R., 2017, In: International Journal of Number Theory. 13, 5, 1349.

  Research output: Contribution to journal › Article › peer-review

• Prescribing the binary digits of squarefree numbers and quadratic residues

  Dietmann, R., Elsholtz, C. & Shparlinski, I., 5 May 2017, (E-pub ahead of print) In: Transactions of the American Mathematical Society. 369, p. 8369-8388

  Research output: Contribution to journal › Article › peer-review

  Open Access
• 2016

  ALMOST ALL PRIMES HAVE A MULTIPLE OF SMALL HAMMING WEIGHT

  ELSHOLTZ, CHRISTIAN., 23 May 2016, In: Bulletin of the Australian Mathematical Society. 94, 2, p. 224-235 12 p.

  Research output: Contribution to journal › Article › peer-review

  • Hamming Weight 100%

• An Alternative Proof on Four-Dimensional Zero-Sums

  Elsholtz, C., 2016, Papers in Number Theory, RMS-Lecture Notes Series. Mysore: Ramanujan Mathematical Society, Vol. 23. p. 29–36

  Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

• Egyptian fractions with odd denominators

  Elsholtz, C., 28 Jun 2016, In: The Quarterly Journal of Mathematics. 67, 3

  Research output: Contribution to journal › Article › peer-review

• Sums of two squares and a power

  Dietmann, R. & Elsholtz, C., 2016, From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz. 1 ed. Springer International Publishing AG , p. 103-108

  Research output: Chapter in Book/Report/Conference proceeding › Chapter
• 2015

  Additive decompositions of sets with restricted prime factors

  Elsholtz, C. & Harper, A. J., 2015, In: Transactions of the American Mathematical Society. 367, p. 7403-7427

  Research output: Contribution to journal › Article › peer-review

• Congruence properties of multiplicative functions on sumsets and monochromatic solutions of linear equations

  Elsholtz, C. & Gunderson, D. S., 2015, In: Functiones et approximatio. 52, 2, p. 263-281

  Research output: Contribution to journal › Article

• Hilbert cubes in arithmetic sets

  Elsholtz, C. & Dietmann, R., 2015, In: Revista Matematica Iberoamericana. 31, 4, p. 1477-1498

  Research output: Contribution to journal › Article › peer-review

• On conjectures of T. Ordowski and Z.W. Sun concerning primes and quadratic forms

  Elsholtz, C. & Harman, G., 2015, Analytic Number Theory (In Honor of Helmut Maier’s 60th Birthday). 1 ed. ., p. 65-81

  Research output: Chapter in Book/Report/Conference proceeding › Chapter
• 2014

  On Diophantine quintuples and D(-1)-quadruples

  Elsholtz, C., Filipin, A. & Fujita, Y., 2014, In: Monatshefte für Mathematik. 175, 2, p. 227-239

  Research output: Contribution to journal › Article › peer-review
• 2013

  Counting the number of solutions to the Erdos-Straus equation on unit fractions

  Elsholtz, C. & Tao, T., 2013, In: Journal of the Australian Mathematical Society . 94, 1, p. 50-105

  Research output: Contribution to journal › Article › peer-review

• On Gaps Between Primitive Roots in the Hamming Metric

  Dietmann, R., Elsholtz, C. & Shparlinski, I., 2013, In: The Quarterly Journal of Mathematics. 64, 4, p. 1043-1055

  Research output: Contribution to journal › Article › peer-review

• On gaps between quadratic non-residues in the Euclidean and Hamming metrics

  Dietmann, R., Elsholtz, C. & Shparlinski, I., 2013, In: Indagationes Mathematicae. 24, 4, p. 930-938

  Research output: Contribution to journal › Article › peer-review

• Sumsets being squares

  Elsholtz, C. & Dujella, A., 2013, In: Acta Mathematica Hungarica. 141, 4, p. 353-357

  Research output: Contribution to journal › Article › peer-review

• The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

  Elsholtz, C., Heuberger, C. & Prodinger, H., 2013, In: IEEE Transactions on Information Theory. 59, 2, p. 1065-1075

  Research output: Contribution to journal › Article › peer-review
• 2012

  A problem of Ramanujan, Erdos and Katai on the iterated divisor function

  Buttkewitz, Y., Elsholtz, C., Ford, K. & Schlage-Puchta, J-C., 2012, In: International Mathematics Research Notices. 2012, 17, p. 4051-4061

  Research output: Contribution to journal › Article › peer-review

• Egyptian fractions with restrictions

  Chen, Y-G., Elsholtz, C. & Jiang, L-L., 2012, In: Acta Arithmetica. 154, 2, p. 109-123

  Research output: Contribution to journal › Article › peer-review

• Hilbert cubes in progression-free sets and in the set of squares

  Dietmann, R. & Elsholtz, C., 2012, In: Israel Journal of Mathematics . 192, 1, p. 59-66

  Research output: Contribution to journal › Article › peer-review

• Prime divisors of thin sequences

  Elsholtz, C., 2012, In: The American Mathematical Monthly. 119, 4, p. 331-333

  Research output: Contribution to journal › Article › peer-review

• The central limit theorem for subsequences in probabilistic number theory

  Aistleitner, C. & Elsholtz, C., 2012, In: Canadian Journal of Mathematics. 64, 6, p. 1201-1221

  Research output: Contribution to journal › Article › peer-review
• 2011

  Patterns and complexity of multiplicative functions

  Elsholtz, C. & Buttkewitz, Y., 2011, In: Journal of the London Mathematical Society. 84, 3, p. 578-594

  Research output: Contribution to journal › Article › peer-review

• The number of representations of rationals as a sum of unit fractions

  Browning, T. & Elsholtz, C., 2011, In: Illinois Journal of Mathematics. 55, 2, p. 685-696

  Research output: Contribution to journal › Article › peer-review
• 2010

  A Combinatorial Approach to Sums of Two Squares and Related Problems

  Elsholtz, C., 2010, Additive Number Theory: Festschrift in Honor of the sixtieth birthday of Melvyn B. Nathanson. 1 ed. Springer Verlag, p. 115-140

  Research output: Chapter in Book/Report/Conference proceeding › Chapter
• 2009

  Independence and interdependence in collective decision making: An agent-based model of nest-site choice by honeybee swarms

  List, C., Elsholtz, C. & Seeley, T. D., 27 Mar 2009, In: Philosophical Transactions of the Royal Society B: Biological Sciences. 364, 1518, p. 755-762 8 p.

  Research output: Contribution to journal › Article › peer-review

  • Group Decision-Making 100%
  • Voting Rule 33%

• Non-simple abelian varieties in a family: Geometric and analytic approaches

  Ellenberg, J. S., Elsholtz, C., Hall, C. & Kowalski, E., Aug 2009, In: Journal of the London Mathematical Society. 80, 1, p. 135-154 20 p.

  Research output: Contribution to journal › Article › peer-review

  • Trivial Group 100%
  • Sieve Theory 100%
  • Abelian Variety 100%
  • Arithmetic Geometry 100%
  • Information 100%
• 2008

  Multiplicative decomposability of shifted sets

  Elsholtz, C., Feb 2008, In: The Bulletin of the London Mathematical Society. 40, 1, p. 97-107 11 p.

  Research output: Contribution to journal › Article › peer-review

  • Largest Element 100%
  • Carmichael number 50%

• The number Γ(k) in Waring's problem

  Elsholtz, C., 2008, In: Acta Arithmetica. 131, 1, p. 43-49 7 p.

  Research output: Contribution to journal › Article › peer-review