Relevant bibliographies by topics / Arithmetic progressions in sumsets

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Arithmetic progressions in sumsets'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Arithmetic progressions in sumsets"

1

Ruzsa, Imre. "Arithmetic progressions in sumsets." Acta Arithmetica 60, no. 2 (1991): 191–202. http://dx.doi.org/10.4064/aa-60-2-191-202.

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Green, B. "Arithmetic progressions in sumsets." Geometric And Functional Analysis 12, no. 3 (August 1, 2002): 584–97. http://dx.doi.org/10.1007/s00039-002-8258-4.

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Erdös, Paul, Melvyn B. Nathanson, and András Sárközy. "Sumsets containing infinite arithmetic progressions." Journal of Number Theory 28, no. 2 (February 1988): 159–66. http://dx.doi.org/10.1016/0022-314x(88)90063-7.

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Sanders, Tom. "Three-term arithmetic progressions and sumsets." Proceedings of the Edinburgh Mathematical Society 52, no. 1 (February 2009): 211–33. http://dx.doi.org/10.1017/s0013091506001398.

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Szemerédi, Endre, and Van Vu. "Finite and infinite arithmetic progressions in sumsets." Annals of Mathematics 163, no. 1 (January 1, 2006): 1–35. http://dx.doi.org/10.4007/annals.2006.163.1.

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SOLYMOSI, JÓZSEF. "Arithmetic Progressions in Sets with Small Sumsets." Combinatorics, Probability and Computing 15, no. 04 (March 6, 2006): 597. http://dx.doi.org/10.1017/s0963548306007516.

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MEI, SHU-YUAN, and YONG-GAO CHEN. "ARITHMETIC PROGRESSIONS IN SUMSETS AND DIFFERENCE SETS." International Journal of Number Theory 09, no. 03 (April 7, 2013): 601–6. http://dx.doi.org/10.1142/s1793042112501503.

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Let s ≥ 1, Ai ⊆ {1,2,…,N} (1 ≤ i ≤ s) and k ≥ 3 be an odd integer. In this paper, one of the main results is: if [Formula: see text], then (a) each of Ai - Aj (1 ≤ i, j ≤ s) contains an arithmetic progression of length k with the same common difference; (b) all sets Ai - Ai (1 ≤ i ≤ s) contain a common arithmetic progression of length k. Finally, we pose several problems for further research.
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Szemerédi, E., and V. Vu. "Long arithmetic progressions in sumsets: Thresholds and bounds." Journal of the American Mathematical Society 19, no. 1 (September 13, 2005): 119–69. http://dx.doi.org/10.1090/s0894-0347-05-00502-3.

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CROOT, ERNIE, IZABELLA ŁABA, and OLOF SISASK. "Arithmetic Progressions in Sumsets and Lp-Almost-Periodicity." Combinatorics, Probability and Computing 22, no. 3 (March 19, 2013): 351–65. http://dx.doi.org/10.1017/s0963548313000060.

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We prove results about the Lp-almost-periodicity of convolutions. One of these follows from a simple but rather general lemma about approximating a sum of functions in Lp, and gives a very short proof of a theorem of Green that if A and B are subsets of {1,. . .,N} of sizes αN and βN then A+B contains an arithmetic progression of length at least \begin{equation} \exp ( c (\alpha \beta \log N)^{1/2} - \log\log N). \end{equation} Another almost-periodicity result improves this bound for densities decreasing with N: we show that under the above hypotheses the sumset A+B contains an arithmetic progression of length at least \begin{equation} \exp\biggl( c \biggl(\frac{\alpha \log N}{\log^3 2\beta^{-1}} \biggr)^{1/2} - \log( \beta^{-1} \log N) \biggr). \end{equation}
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Nathanson, Melvyn, and András Sárközy. "Sumsets containing long arithmetic progressions and powers of 2." Acta Arithmetica 54, no. 2 (1989): 147–54. http://dx.doi.org/10.4064/aa-54-2-147-154.

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Dissertations / Theses on the topic "Arithmetic progressions in sumsets"

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Henriot, Kevin. "Structures linéaires dans les ensembles à faible densité." Thèse, Paris 7, 2014. http://hdl.handle.net/1866/11116.

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Réalisé en cotutelle avec l'Université Paris-Diderot.
Nous présentons trois résultats en combinatoire additive, un domaine récent à la croisée de la combinatoire, l'analyse harmonique et la théorie analytique des nombres. Le thème unificateur de notre thèse est la détection de structures additives dans les ensembles arithmétiques à faible densité, avec un intérêt particulier pour les aspects quantitatifs. Notre première contribution est une estimation de densité améliorée pour le problème, initié entre autres par Bourgain, de trouver une longue progression arithmétique dans un ensemble somme triple. Notre deuxième résultat consiste en une généralisation des bornes de Sanders pour le théorème de Roth, du cas d'un ensemble dense dans les entiers à celui d'un ensemble à faible croissance additive dans un groupe abélien arbitraire. Finalement, nous étendons les meilleures bornes quantitatives connues pour le théorème de Roth dans les premiers, à tous les systèmes d'équations linéaires invariants par translation et de complexité un.
We present three results in additive combinatorics, a recent field at the interface of combinatorics, harmonic analysis and analytic number theory. The unifying theme in our thesis is the detection of additive structure in arithmetic sets of low density, with an emphasis on quantitative aspects. Our first contribution is an improved density estimate for the problem, initiated by Bourgain and others, of finding a long arithmetic progression in a triple sumset. Our second result is a generalization of Sanders' bounds for Roth's theorem from the dense setting, to the setting of small doubling in an arbitrary abelian group. Finally, we extend the best known quantitative results for Roth's theorem in the primes, to all translation-invariant systems of equations of complexity one.
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Shiu, Daniel Kai Lun. "Prime numbers in arithmetic progressions." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318815.

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Rimanić, Luka. "Arithmetic progressions, corners and loneliness." Thesis, University of Bristol, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761230.

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張勁光 and King-kwong Cheung. "Prime solutions in arithmetic progressions of some linear ternary equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B42575874.

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Cheung, King-kwong. "Prime solutions in arithmetic progressions of some linear ternary equations." Click to view the E-thesis via HKUTO, 2000. http://sunzi.lib.hku.hk/hkuto/record/B42575874.

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White, Christopher J. "Finding primes in arithmetic progressions and estimating double exponential sums." Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707745.

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Dyer, A. K. "Applications of sieve methods in number theory." Thesis, Bucks New University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384646.

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Coleman, Mark David. "Topics in the distribution of primes." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293491.

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樊家榮 and Ka-wing Fan. "Prime solutions in arithmetic progressions of some quadratic equationsand linear equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31225962.

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Vlasic, Andrew. "A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4476/.

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We follow a research paper that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.
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Books on the topic "Arithmetic progressions in sumsets"

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A course in analytic number theory. Providence, Rhode Island: American Mathematical Society, 2014.

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Florian, Luca, ed. Analytic number theory: Exploring the anatomy of integers. Providence, R.I: American Mathematical Society, 2012.

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Knafo, Emmanuel Robert. Variance of distribution of almost primes in arithmetic progressions. 2006.

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John, Friedlander, ed. Oscillation theorems for primes in arithmetic progressions and for sifting functions. Toronto: Dept. of Mathematics, University of Toronto, 1989.

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Mee, Nicholas. Celestial Tapestry. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851950.001.0001.

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Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.
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Book chapters on the topic "Arithmetic progressions in sumsets"

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Cilleruelo, Javier, and Andrew Granville. "Lattice points on circles, squares in arithmetic progressions and sumsets of squares." In CRM Proceedings and Lecture Notes, 241–62. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/crmp/043/12.

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Gelfand, Israel M., and Alexander Shen. "Arithmetic progressions." In Algebra, 77–79. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_39.

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Landman, Bruce, and Aaron Robertson. "Arithmetic progressions (𝑚𝑜𝑑𝑚)." In The Student Mathematical Library, 183–201. Providence, Rhode Island: American Mathematical Society, 2014. http://dx.doi.org/10.1090/stml/073/06.

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Harzheim, Egbert. "Almost Arithmetic Progressions." In Numbers, Information and Complexity, 17–20. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-6048-4_2.

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Murty, M. Ram. "Primes in Arithmetic Progressions." In Problems in Analytic Number Theory, 211–45. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3441-6_12.

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Murty, M. Ram. "Primes in Arithmetic Progressions." In Problems in Analytic Number Theory, 17–33. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3441-6_2.

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Landman, Bruce, and Aaron Robertson. "Arithmetic progressions (mod 𝑚)." In The Student Mathematical Library, 163–80. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/stml/024/06.

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Ribenboim, Paulo. "Primes in Arithmetic Progressions." In Classical Theory of Algebraic Numbers, 523–42. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-0-387-21690-4_24.

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Gowers, W. Timothy. "Erdős and Arithmetic Progressions." In Bolyai Society Mathematical Studies, 265–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39286-3_8.

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Friedlander, J. B., and H. Iwaniec. "Norms in Arithmetic Progressions." In Progress in Mathematics, 265–68. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-3464-7_17.

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Conference papers on the topic "Arithmetic progressions in sumsets"

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Coppersmith, D., and S. Winograd. "Matrix multiplication via arithmetic progressions." In the nineteenth annual ACM conference. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/28395.28396.

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Babaali, M., and M. Egerstedt. "Pathwise observability through arithmetic progressions and non-pathological sampling." In Proceedings of the 2004 American Control Conference. IEEE, 2004. http://dx.doi.org/10.23919/acc.2004.1384786.

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CUI, ZHEN, and BOQING XUE. "A NOTE ON THE DISTRIBUTION OF PRIMES IN ARITHMETIC PROGRESSIONS." In Proceedings of the 6th China–Japan Seminar. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814452458_0004.

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Gomes, Ane Caroline, Brendoon Ryos, Gustavo Rodrigues, and Joaquim Pessoa Filho. "Space chain: A math game for training geometric and arithmetic progressions." In 2018 IEEE Global Engineering Education Conference (EDUCON). IEEE, 2018. http://dx.doi.org/10.1109/educon.2018.8363480.

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Srikanth, Ch. "PhD Forum 2017 New Cryptographic Systems Based on Certain Sequences of Arithmetic Progressions." In 2017 23RD Annual International Conference in Advanced Computing and Communications (ADCOM). IEEE, 2017. http://dx.doi.org/10.1109/adcom.2017.00016.

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