| 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. | pdf 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 The paper is top ten in the most downloaded of the journal in 2009. 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, appeared in: Additive Number Theory: Festschrift in Honor of the sixtieth birthday of Melvyn B. Nathanson, Springer Verlag, 2010, pages 115-140. | |||
| 31 | Hilbert cubes in progression-free sets and in the set of squares | with R. Dietmann | Israel Journal of Mathematics, to appear | ||
| 32 | Prime divisors of thin sequences | American Mathematical Monthly, Vol. 119, No. 4 (April 2012), pp. 331-333 | JSTOR | 33 | The number of representations of rationals as a sum of unit fractions | with Tim Browning | to appear in Illinois J of Mathematics | 34 | Monochromatic solutions of linear equations. | with Frank Weber | submitted | 35 | Patterns and complexity of multiplicative functions | with Yvonne Buttkewitz | Journal of the London Mathematical Society 84 (3) 2011, 578-594. | 36 | A problem of Ramanujan, Erdos and Katai on the iterated divisor function | with Yvonne Buttkewitz, Kevin Ford, Jan-Christoph Schlage-Puchta | to appear in IMRN | arxiv | 37 | Egyptian fractions with restrictions | with Yong-Gao Chen and Li-Li Jiang (Nanjing, China) | to appear in Acta Arithmetica | arxiv | 38 | The central limit theorem for subsequences in probabilistic number theory | with Christoph Aistleitner | to appear in Canadian Journal of Mathematics | 39 | Counting the number of solutions to the Erdos-Straus equation on unit fractions | with Terence Tao | submitted | arxiv | 40 | The number of Huffman codes, compact trees, and sums of unit fractions | with Clemens Heuberger, Helmut Prodinger | submitted | arxiv |
Papers on prime numbers: 1,2,4,6,7,9,10,12,13,14,17,22,25,29,30,32
Papers using sieve methods: 2,3,4,5,6,7,13,16,17,22,25,27,29
Papers on arithmetic functions: 35, 36
Papers on zero sums: 8,15,21
Papers on diophantine equations, Waring's problem: 3,24,26,34, 37
Papers in combinatorics: 8,9,14,15,18,19,20,21,34,35
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,
to appear in Israel Journal of Mathematics.
35. Patterns and complexity of multiplicative functions, with Yvonne Buttkewitz, to
appear in Journal of the London Mathematical Society
36. A problem of Ramanujan, Erdos and Katai on the iterated
divisor function, with Yvonne Buttkewitz, Kevin Ford, Jan-Christoph Schlage-Puchta
