Relevant bibliographies by topics / Arithmetic progressions in sumsets / Journal articles
To see the other types of publications on this topic, follow the link: Arithmetic progressions in sumsets.

Journal articles on the topic 'Arithmetic progressions in sumsets'

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

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Arithmetic progressions in sumsets.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
8

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

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.

Full text
Abstract:
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}
APA, Harvard, Vancouver, ISO, and other styles
10

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.

Full text
APA, Harvard, Vancouver, ISO, and other styles
11

Ruzsa, I. Z. "Generalized arithmetical progressions and sumsets." Acta Mathematica Hungarica 65, no. 4 (December 1994): 379–88. http://dx.doi.org/10.1007/bf01876039.

Full text
APA, Harvard, Vancouver, ISO, and other styles
12

Tao, Terence, and Van Vu. "John-type theorems for generalized arithmetic progressions and iterated sumsets." Advances in Mathematics 219, no. 2 (October 2008): 428–49. http://dx.doi.org/10.1016/j.aim.2008.05.002.

Full text
APA, Harvard, Vancouver, ISO, and other styles
13

SANDERS, TOM. "Additive structures in sumsets." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 2 (March 2008): 289–316. http://dx.doi.org/10.1017/s030500410700093x.

Full text
Abstract:
AbstractSuppose that A and A′ are subsets of ℤ/Nℤ. We write A+A′ for the set {a+a′:a ∈ A and a′ ∈ A′} and call it the sumset of A and A′. In this paper we address the following question. Suppose that A1,. . .,Am are subsets of ℤ/Nℤ. Does A1+· · ·+Am contain a long arithmetic progression?The situation for m=2 is rather different from that for m ≥ 3. In the former case we provide a new proof of a result due to Green. He proved that A1+A2 contains an arithmetic progression of length roughly $\exp (c\sqrt{\alpha_1\alpha_2 \log N})$ where α1 and α2 are the respective densities of A1 and A2. In the latter case we improve the existing estimates. For example we show that if A ⊂ ℤ/Nℤ has density $\alpha \gg \sqrt{\log \log N/\log N}$ then A+A+A contains an arithmetic progression of length Ncα. This compares with the previous best of Ncα2+ϵ.Two main ingredients have gone into the paper. The first is the observation that one can apply the iterative method to these problems using some machinery of Bourgain. The second is that we can localize a result due to Chang regarding the large spectrum of L2-functions. This localization seems to be of interest in its own right and has already found one application elsewhere.
APA, Harvard, Vancouver, ISO, and other styles
14

Freiman, Gregory A. "Inverse Additive Number Theory. XI. Long arithmetic progressions in sets with small sumsets." Acta Arithmetica 137, no. 4 (2009): 325–31. http://dx.doi.org/10.4064/aa137-4-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
15

Guo, Shu-Guang, and Yong-Gao Chen. "Blocks of consecutive integers in sumsets (A + B)t." Bulletin of the Australian Mathematical Society 70, no. 2 (October 2004): 283–91. http://dx.doi.org/10.1017/s000497270003450x.

Full text
Abstract:
Let A, B ⊆ {1, …, n}. For m ∈ Z, let rA,B(m) be the cardinality of the set of ordered pairs (a, b) ∈ A × B such that a + b = m. For t ≥ 1, denote by (A + B)t the set of the elements m for which rA, B(m) ≥ t. In this paper we prove that for any subsets A, B ⊆ {1, …, n} such that |A| + |B| ≥ (4n + 4t − 3)/3, the sumset (A + B)t contains a block of consecutive integers with the length at least |A| + |B| − 2t + 1, and that (a) for any two subsets A and B of {1, …, n} such that |A| + |B| ≥ (4n)/3, there exists an arithmetic progression of length n in A + B; (b) for any 2 ≤ r ≤ (4n − 1)/3, there exist two subsets A and B of {1, …, n} with |A| + |B| = r such that any arithmetic progression in A + B has the length at most (2n − 1)/3 + 1.
APA, Harvard, Vancouver, ISO, and other styles
16

Ahmadi, Omran, and Igor E. Shparlinski. "Geometric progressions in sumsets over finite fields." Monatshefte für Mathematik 152, no. 3 (June 1, 2007): 177–85. http://dx.doi.org/10.1007/s00605-007-0471-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
17

Balog, A., J. Rivat, and A. Sárközy. "On arithmetic properties of sumsets." Acta Mathematica Hungarica 144, no. 1 (August 28, 2014): 18–42. http://dx.doi.org/10.1007/s10474-014-0436-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
18

Hajdu, L. "Powerful arithmetic progressions." Indagationes Mathematicae 19, no. 4 (December 2008): 547–61. http://dx.doi.org/10.1016/s0019-3577(09)00012-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
19

Butler, Steve, Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard L. Kramer, Jephian Chin-Hung Lin, et al. "Rainbow arithmetic progressions." Journal of Combinatorics 7, no. 4 (2016): 595–626. http://dx.doi.org/10.4310/joc.2016.v7.n4.a3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
20

Shparlinski, Igor E. "Geometric progressions in vector sumsets over finite fields." Finite Fields and Their Applications 68 (December 2020): 101747. http://dx.doi.org/10.1016/j.ffa.2020.101747.

Full text
APA, Harvard, Vancouver, ISO, and other styles
21

Elliott, P. D. T. A. "Additive Arithmetic Functions on Arithmetic Progressions." Proceedings of the London Mathematical Society s3-54, no. 1 (January 1987): 15–37. http://dx.doi.org/10.1112/plms/s3-54.1.15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
22

Chen, Yong-Gao. "On disjoint arithmetic progressions." Acta Arithmetica 118, no. 2 (2005): 143–48. http://dx.doi.org/10.4064/aa118-2-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
23

Downarowicz, T. "Reading along arithmetic progressions." Colloquium Mathematicum 80, no. 2 (1999): 293–96. http://dx.doi.org/10.4064/cm-80-2-293-296.

Full text
APA, Harvard, Vancouver, ISO, and other styles
24

Matoušek, Jiří, and Joel Spencer. "Discrepancy in arithmetic progressions." Journal of the American Mathematical Society 9, no. 1 (1996): 195–204. http://dx.doi.org/10.1090/s0894-0347-96-00175-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
25

Bombieri, Enrico, Andrew Granville, and J�nos Pintz. "Squares in arithmetic progressions." Duke Mathematical Journal 66, no. 3 (June 1992): 369–85. http://dx.doi.org/10.1215/s0012-7094-92-06612-9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
26

Ramaré, Olivier, and Robert Rumely. "Primes in arithmetic progressions." Mathematics of Computation 65, no. 213 (January 1, 1996): 397–426. http://dx.doi.org/10.1090/s0025-5718-96-00669-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
27

Harzheim, Egbert. "On weakly arithmetic progressions." Discrete Mathematics 138, no. 1-3 (March 1995): 255–60. http://dx.doi.org/10.1016/0012-365x(94)00207-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
28

Hajdu, Lajos, and Szabolcs Tengely. "Powers in arithmetic progressions." Ramanujan Journal 55, no. 3 (January 30, 2021): 965–86. http://dx.doi.org/10.1007/s11139-020-00331-5.

Full text
Abstract:
AbstractWe investigate the function $$P_{a,b;N}(\ell )$$ P a , b ; N ( ℓ ) describing the number of $$\ell $$ ℓ -th powers among the first N terms of an arithmetic progression $$ax+b$$ a x + b . We completely describe the arithmetic progressions containing the most $$\ell $$ ℓ -th powers asymptotically. Based on these results we formulate problems concerning the maximum of $$P_{a,b;N}(\ell )$$ P a , b ; N ( ℓ ) , and we give affirmative answers to these questions for certain small values of $$\ell $$ ℓ and N.
APA, Harvard, Vancouver, ISO, and other styles
29

Mikawa, Hiroshi. "On primes in arithmetic progressions." Tsukuba Journal of Mathematics 25, no. 1 (June 2001): 121–53. http://dx.doi.org/10.21099/tkbjm/1496164216.

Full text
APA, Harvard, Vancouver, ISO, and other styles
30

Puchta, Jan-Christoph. "Primes in short arithmetic progressions." Acta Arithmetica 106, no. 2 (2003): 143–49. http://dx.doi.org/10.4064/aa106-2-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
31

Croot, Ernest S. "On non-intersecting arithmetic progressions." Acta Arithmetica 110, no. 3 (2003): 233–38. http://dx.doi.org/10.4064/aa110-3-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
32

Getz, Marty, Dixon Jones, and Ken Dutch. "Partitioning by Arithmetic Progressions: 11005." American Mathematical Monthly 112, no. 1 (January 1, 2005): 89. http://dx.doi.org/10.2307/30037399.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Getz, Marty, and Dixon Jones. "Errata: Partitioning by Arithmetic Progressions." American Mathematical Monthly 112, no. 10 (December 1, 2005): 936. http://dx.doi.org/10.2307/30037652.

Full text
APA, Harvard, Vancouver, ISO, and other styles
34

Londner, Itay, and Alexander Olevskiĭ. "Riesz sequences and arithmetic progressions." Studia Mathematica 225, no. 2 (2014): 183–91. http://dx.doi.org/10.4064/sm225-2-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
35

Dlab, Vlastimil. "Arithmetic progressions of higher order." Teaching Mathematics and Computer Science 9, no. 2 (2011): 225–39. http://dx.doi.org/10.5485/tmcs.2011.0281.

Full text
APA, Harvard, Vancouver, ISO, and other styles
36

AGUIRRE, JULIAN, ANDREJ DUJELLA, and JUAN CARLOS PERAL. "Arithmetic progressions and Pellian equations." Publicationes Mathematicae Debrecen 83, no. 4 (December 1, 2013): 683–95. http://dx.doi.org/10.5486/pmd.2013.5684.

Full text
APA, Harvard, Vancouver, ISO, and other styles
37

Baildon, John D. "Arithmetic Progressions and the Consumer." College Mathematics Journal 16, no. 5 (November 1985): 395. http://dx.doi.org/10.2307/2686999.

Full text
APA, Harvard, Vancouver, ISO, and other styles
38

Pethő, A., and V. Ziegler. "Arithmetic progressions on Pell equations." Journal of Number Theory 128, no. 6 (June 2008): 1389–409. http://dx.doi.org/10.1016/j.jnt.2008.01.003.

Full text
APA, Harvard, Vancouver, ISO, and other styles
39

Nunes, Ramon M. "Squarefree numbers in arithmetic progressions." Journal of Number Theory 153 (August 2015): 1–36. http://dx.doi.org/10.1016/j.jnt.2014.12.025.

Full text
APA, Harvard, Vancouver, ISO, and other styles
40

Coppersmith, Don, and Shmuel Winograd. "Matrix multiplication via arithmetic progressions." Journal of Symbolic Computation 9, no. 3 (March 1990): 251–80. http://dx.doi.org/10.1016/s0747-7171(08)80013-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
41

MATOMÄKI, KAISA. "CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS." Journal of the Australian Mathematical Society 94, no. 2 (March 8, 2013): 268–75. http://dx.doi.org/10.1017/s1446788712000547.

Full text
Abstract:
AbstractWe prove that when $(a, m)= 1$ and $a$ is a quadratic residue $\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$, there are infinitely many Carmichael numbers in the arithmetic progression $a\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$. Indeed the number of them up to $x$ is at least ${x}^{1/ 5} $ when $x$ is large enough (depending on $m$).
APA, Harvard, Vancouver, ISO, and other styles
42

Baildon, John D. "Arithmetic Progressions and the Consumer." College Mathematics Journal 16, no. 5 (November 1985): 395–97. http://dx.doi.org/10.1080/07468342.1985.11972913.

Full text
APA, Harvard, Vancouver, ISO, and other styles
43

Yuster, Raphael. "Arithmetic progressions with constant weight." Discrete Mathematics 224, no. 1-3 (September 2000): 225–37. http://dx.doi.org/10.1016/s0012-365x(00)00048-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
44

Walker, Aled, and Alexander Walker. "Arithmetic Progressions with Restricted Digits." American Mathematical Monthly 127, no. 2 (January 6, 2020): 140–50. http://dx.doi.org/10.1080/00029890.2020.1682888.

Full text
APA, Harvard, Vancouver, ISO, and other styles
45

Hildebrand, Adolf. "Additive Functions on Arithmetic Progressions." Journal of the London Mathematical Society s2-34, no. 3 (December 1986): 394–402. http://dx.doi.org/10.1112/jlms/s2-34.3.394.

Full text
APA, Harvard, Vancouver, ISO, and other styles
46

Hare, Kathryn E., and L. Thomas Ramsey. "Kronecker Constants of Arithmetic Progressions." Experimental Mathematics 23, no. 4 (October 2, 2014): 414–22. http://dx.doi.org/10.1080/10586458.2014.928656.

Full text
APA, Harvard, Vancouver, ISO, and other styles
47

Lewulis, Paweł. "Chen primes in arithmetic progressions." Acta Arithmetica 182, no. 4 (2018): 301–10. http://dx.doi.org/10.4064/aa8417-1-2017.

Full text
APA, Harvard, Vancouver, ISO, and other styles
48

de la Bretèche, Régis, Kevin Ford, and Joseph Vandehey. "On non-intersecting arithmetic progressions." Acta Arithmetica 157, no. 4 (2013): 381–92. http://dx.doi.org/10.4064/aa157-4-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
49

Murty, Ram, and Nithum Thain. "Primes in Certain Arithmetic Progressions." Functiones et Approximatio Commentarii Mathematici 35 (January 2006): 249–59. http://dx.doi.org/10.7169/facm/1229442627.

Full text
APA, Harvard, Vancouver, ISO, and other styles
50

Friedlander, John B., and Henryk Iwaniec. "Gaussian sequences in arithmetic progressions." Functiones et Approximatio Commentarii Mathematici 37, no. 1 (January 2007): 149–57. http://dx.doi.org/10.7169/facm/1229618747.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the bibliographies on the topic 'Arithmetic progressions in sumsets' for other source types:
Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography