| Qualification Theses | ||
| The Erdos-Straus conjecture | Diplomarbeit (Master Thesis equivalent) | |
| Sums of k unit fractions | Ph.D. Thesis (parts appeared in Transactions of the AMS) | |
| Combinatorial Prime Number Theory | Habilitationsschrift (Postdoc Thesis). (External referees: Brüdern (Stuttgart), Heath-Brown (Oxford), A. Sárközy (Budapest). Internal referees: Lucht, Hilgert). |
| Title | Abstract | Coauthor(s) | Status | Download | |
| 1 | Primzahlen der Form $p=4k+1$ sind Summe von zwei Quadratzahlen | Mathematik Lehren. (Februar 1994, Heft 62, 58-61) | |||
| 2 | A remark on Hofmann and Wolke's additive decompositions of the set of primes. | Arch. Math. 76, No.1, 30-33 (2001). | Link to publisher Springer Link pdf | ||
| 3 | Sums of $k$ unit fractions | Trans. Amer. Math. Soc. 353 (2001), no. 8, 3209-3227. | Transactions of the AMS dvi ps pdf | ||
| 4 | The inverse Goldbach problem | Mathematika 48 (2001), 151-158 | dvi ps pdf scanned pdf | ||
| 5 | The distribution of sequences in residue classes | Proc. Amer. Math. Soc. 130 (2002), no.8, 2247-2250 | Proceedings of the AMS dvi ps pdf | ||
| 6 | Some remarks on the additive structure of the set of primes | Number theory for the millennium, I (Urbana, IL, 2000), 419--427, (Proceedings of the Millennial Conference on Number Theory (Bennett et.al.), AK Peters, 2002). | ps pdf | ||
| 7 | Upper bounds for prime $k$-tuples of size $\log N$ and oscillations | Arch. Math. 82 (2004), 33-39. | Link to publisher ps pdf | ||
| 8 | Lower bounds for multidimensional zero sums | Combinatorica 24, (2004) no. 3, 351 - 358. | Link to publisher dvi ps pdf | ||
| 9 | Triples of primes in arithmetic progressions | Quart. J. Math. 53 (2002), 393-395. | Link to publisher pdf ps | ||
| 10 |
The Liouville---Heath-Brown---Zagier
proof of the two squares theorem
Kombinatorische Beweise des Zweiquadratesatzes und Verallgemeinerungen |
The english version contains all details of the proofs. The German version has a more general introduction and is directed towards a general audience and contains another short proof. The German version is published in Mathematische Semesterberichte 50, Heft 1, 77-93, 2003. | English preprint.
ps
German version pdf Link to publisher |
||
| 11 | Zeroes of $L$-functions attached to cuspidal representation of congruence subgroups of $GL_n (\mathbb{Z})$ | Jacek Pomykala, Warsaw | submitted, Preprint | ||
| 12 | On primes of the form $x^2+y^4$ | submitted, Preprint | |||
| 13 | On cluster primes | Acta Arithmetica, 110 (2003), 281-284. | Link to publisher dvi ps pdf | 14 | Von Lücken zwischen Primzahlen zur Optimierung von Gitterpunkten. | Survey for a general audience (in German) | invited paper by TU Contact, magazine of the TU Clausthal, issue 12, 2003, pages 61-64 |
1) zum
Heft
2) pdf 3) internet links that are mentioned in the paper |
| 15 | A short survey on upper and lower bounds for multidimensional zero sums | This survey appeared with years of delay. For an update see "Zero-sum problems in finite abelian groups and affine caps" below. | Springer Lecture Notes in Computer Science, LNCS 4123, pages 1079-1080, 2006. |
pdf
Link to the publisher |
|
| 16 | On variants of the larger sieve | Ernie Croot, Georgia Tech. | Acta Mathematica Hungarica 103 (3) (2004) 243-254 | Link to publisher ps pdf | |
| 17 | On Thin Sets of Primes Expressible as Sumsets | Ernie Croot, Georgia Tech. | Acta Mathematica Hungarica, 106 (3), 2005, 197 - 226 | Link to publisher ps pdf | |
| 18 | A simple proof of Sen's possibility theorem on majority decisions | C. List, LSE, London | Elemente der Mathematik 60 (2005), 45-56. | Link to publisher pdf | |
| 19 | Shifted products that are coprime pure powers | Rainer Dietmann, Stuttgart; Katalin Gyarmati and Miki Simonovits, Budapest | Journal of combinatorial Theory, Series A, 111 (1), 2005, 24-36. | Link to publisher ps pdf | 20 | Maximal dimension of unit simplices | Walter Klotz | Discrete Comput. Geom. 34 (2005), no. 1, 167--177. | Link to publisher dvi ps pdf | 21 | Zero-sum problems in finite abelian groups and affine caps | Yves Edel, Alfred Geroldinger, Silke Kubertin, Laurence Rackham | Quarterly Journal of Mathematics 58 (2007), 159-186 | Link to publisher pdf | 22 | Additive decomposability of multiplicatively defined sets | This paper was invited for an issue at the occasion of the 75th birthday of Prof. Wirsing. Functiones et Approximatio 35 (2006), 61-77. |
Link to publisher |
23 | Sudoku im Mathematikunterricht | A. Mütze | Mathematische Semesterberichte 54 (1), 2007, 69-93 |
Published at Springerlink:
DOI:10.1007/s00591-006-0014-7
An extended version is posted here. Also the internetlinks can be reached from here. |
| 24 | The number Gamma(k) in Waring's problem | Acta Arith. 131 (2008), 43-49 | pdf Acta Arithmetica | ||
| 25 | Multiplicative decomposability of shifted sets | Bulletin of the London Mathematical Society 2008, 40: 97-107 | pdf publisher's site | ||
| 26 | Sums of two squares and one biquadrate | Rainer Dietmann, Stuttgart | Funct. Approx. Comment. Math. Volume 38, Number 2 (2008), 233-234. | publisher's site | |
| 27 | Non-simple abelian varieties in a family: geometric and analytic approaches | with J.Ellenberg (Madison, WI), C.Hall (U o Michigan, Ann Arbor), E.Kowalski (ETH Zürich) | Journal of the LMS 2009 80(1), 135-154 | available on Archiv, Link to Publisher | 28 | Independence and interdependence in collective decision making: an agent-based model of nest-site choice by honeybee swarms | with C.List (LSE), T.D.Seeley (Cornell) | Phil. Trans. R. Soc. B Volume 364, Number 1518 / March 27, 2009 |
Publisher,
pdf Press coverage: Daily Telegraph, Economist, Economist BBC Radio Wales, Friday 13th February 2009, 4.56pm (Good Evening Wales) Recommended by F1000 biology I am mentioned (as a mathematician, albeit not by name) in the cover story of Science News: Swarm Savvy How bees, ants and other animals avoid dumb collective decisions By Susan Milius May 9th, 2009; Vol.175 #10 (p. 16) Science News Cover |
29 | A survey on additive and multiplicative decompositions of sumsets and of shifted sets | Chapter in "Combinatorial Number Theory and Additive Group Theory" Series: Advanced Courses in Mathematics - CRM Barcelona, Geroldinger, Alfred, Ruzsa, Imre Z. 2009, Birkhäuser, (based on the DocCourse on Additive Combinatorics, Barcelona 2008). Pages, 213-231. Publisher |
| 30 | A combinatorial approach to sums of two squares and related problems | Invited paper | |||
| 31 | Hilbert cubes in progression-free sets and in the set of squares | with R. Dietmann | submitted | ||
| 32 | Prime divisors of thin sequences | submitted | 33 | Sums of unit fractions | with Tim Browning | submitted |
Papers on prime numbers: 1,2,4,6,7,9,10,12,13,14,17,22,25,29,30,32
Papers using sieve methds: 2,3,4,5,6,7,13,16,17,22,25,27,29
Papers on zero sums: 8,15,21
Papers on diophantine equations, Waring's problem: 3,24,26
Papers in combinatorics: 8,9,14,15,18,19,20,21
Papers in algebra: 20,21,27
Papers for general audience (e.g. teachers): 1,10,14,18,23,28,30
Papers in 2001: 2,3,4
Papers in 2002: 5,6,9
Papers in 2003: 10,13,14
Papers in 2004: 7,8,16
Papers in 2005: 17,18,19,20
Papers in 2006: 15,22
Papers in 2007: 21,23
Papers in 2008: 24,25,26
Papers in 2009: 27,28,29
Key publications include:
3 Sums of $k$ unit fractions. Trans. Amer. Math. Soc. 353 (2001), no. 8, 3209--3227.2)
4. The inverse Goldbach problem. Mathematika 48 (2001), 151-158.
8. Lower bounds for multidimensional zero sums. Combinatorica 24 (2004), no. 3, 351 -358.
21. Zero-sum problems in finite abelian groups and affine caps, (with Y. Edel (Heidelberg), A.
Geroldinger (Graz), S. Kubertin, L. Rackham), Quarterly J. Math. (Oxford) 58 (2007),
159-186.
25. The multiplicative decomposability of shifted sets, Bulletin of the London Mathematical
Society 40 (2008), 97-107.
27. Non-simple abelian varieties in a family: geometric and analytic approaches, with J.
Ellenberg (Wisconsin, Madison), C. Hall (U of Michigan), E. Kowalski (ETH Zurich). J. London
Math. Soc. (2) 80 (2009), 135-154.
28. Independence and interdependence in collective decision-making: an agent-based model of
nest-site choice by honey bee swarms, with C. List (LSE), T.D. Seeley (Cornell), Phil. Trans.
R. Soc. B Volume 364, Number 1518 / March 2009.
31. Hilbert cubes in progresson-free sets and in the set of squares, with Rainer Dietmann,
submitted.
Last modified: September 2009
