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Journal articles on the topic 'Roth's theorem'

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Published: 4 June 2021
Last updated: 10 February 2022

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1

Sanders, Tom. "On Roth's theorem on progressions." Annals of Mathematics 174, no. 1 (July 1, 2011): 619–36. http://dx.doi.org/10.4007/annals.2011.174.1.20.

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2

Gasbarri, C., and Michael McQuillan. "Roth's theorem for ruled surfaces." American Journal of Mathematics 127, no. 3 (2005): 471–92. http://dx.doi.org/10.1353/ajm.2005.0020.

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3

Gross, Robert. "A note on Roth's Theorem." Journal of Number Theory 36, no. 1 (September 1990): 127–32. http://dx.doi.org/10.1016/0022-314x(90)90010-o.

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4

Ward, A. J. B. "Roth's removal theorem for lambda matrices." International Journal of Mathematical Education in Science and Technology 29, no. 3 (May 1998): 325–28. http://dx.doi.org/10.1080/0020739980290302.

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5

Bombieri, E., and A. J. van der Poorten. "Some quantitative results related to Roth's Theorem." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 2 (October 1988): 233–48. http://dx.doi.org/10.1017/s1446788700030159.

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AbstractWe employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.
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6

Mirek, Mariusz. "Roth's theorem in the Piatetski-Shapiro primes." Revista Matemática Iberoamericana 31, no. 2 (2015): 617–56. http://dx.doi.org/10.4171/rmi/848.

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7

Naslund, Eric. "ON IMPROVING ROTH'S THEOREM IN THE PRIMES." Mathematika 61, no. 1 (October 9, 2014): 49–62. http://dx.doi.org/10.1112/s0025579314000175.

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8

Wang, Julie Tzu-Yueh. "An Effective Roth's Theorem for Function Fields." Rocky Mountain Journal of Mathematics 26, no. 3 (September 1996): 1225–34. http://dx.doi.org/10.1216/rmjm/1181072046.

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9

Liu, Yu-Ru, and Xiaomei Zhao. "A generalization of Roth's theorem in function fields." Michigan Mathematical Journal 61, no. 4 (November 2012): 839–66. http://dx.doi.org/10.1307/mmj/1353098515.

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10

Ru, Min. "A Weak Effective Roth's Theorem over Function Fields." Rocky Mountain Journal of Mathematics 30, no. 2 (June 2000): 723–34. http://dx.doi.org/10.1216/rmjm/1022009292.

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11

Bombieri, E., and A. J. Van Der Poorten. "Some quantitative results related to Roth's theorem: Corrigenda." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 48, no. 1 (February 1990): 154–55. http://dx.doi.org/10.1017/s1446788700035291.

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12

Schmidt, Wolfgang M. "The number of exceptional approximations in Roth's theorem." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 3 (December 1995): 375–83. http://dx.doi.org/10.1017/s1446788700037277.

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AbstractRoth's Theorem says that given ρ < 2 and an algebraic number α, all but finitely many rational numbers x/y satisfy |α - (x/y)|< |y|-ρ. We give upper bounds for the number of these exceptional rationals when 3 ≤ ρ ≤ d, where d is the degree of α. Our result suplements bounds given by Bombieri and Van der Poorten when 2 > ρ ≤ 3; naturally the bounds become smaller as ρ increases.
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13

LIU, YU-RU, and CRAIG V. SPENCER. "A GENERALIZATION OF ROTH'S THEOREM IN FUNCTION FIELDS." International Journal of Number Theory 05, no. 07 (November 2009): 1149–54. http://dx.doi.org/10.1142/s1793042109002602.

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Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q, and let [Formula: see text] denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than N. For non-zero elements r1, …, rs of 𝔽q satisfying r1 + ⋯ + rs = 0, let [Formula: see text] denote the maximal cardinality of a set [Formula: see text] which contains no non-trivial solution of r1x1 + ⋯ + rsxs = 0 with xi ∈ A (1 ≤ i ≤ s). We prove that [Formula: see text].
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14

Schoen, Tomasz. "Improved bound in Roth's theorem on arithmetic progressions." Advances in Mathematics 386 (August 2021): 107801. http://dx.doi.org/10.1016/j.aim.2021.107801.

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15

Liu, Yu-Ru, Craig V. Spencer, and Xiaomei Zhao. "Roth's theorem on systems of linear forms in function fields." Acta Arithmetica 142, no. 4 (2010): 377–86. http://dx.doi.org/10.4064/aa142-4-6.

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16

DOUSSE, JEHANNE. "On a generalisation of Roth's theorem for arithmetic progressions and applications to sum-free subsets." Mathematical Proceedings of the Cambridge Philosophical Society 155, no. 2 (June 12, 2013): 331–41. http://dx.doi.org/10.1017/s0305004113000327.

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AbstractWe prove a generalisation of Roth's theorem for arithmetic progressions to d-configurations, which are sets of the form {ni+nj+a}1 ≤ i ≤ j ≤ d with a, n1,. . .,nd ∈ $\mathbb{N}$, using Roth's original density increment strategy and Gowers uniformity norms. Then we use this generalisation to improve a result of Sudakov, Szemerédi and Vu about sum-free subsets [10] and prove that any set of n integers contains a sum-free subset of size at least logn(log(3)n)1/32772 − o(1).
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17

Huang, Liping, and Jianzhou Liu. "The extension of Roth's theorem for matrix equations over a ring." Linear Algebra and its Applications 259 (July 1997): 229–35. http://dx.doi.org/10.1016/s0024-3795(96)00286-8.

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18

Bloom, T. F. "A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1." Journal of the London Mathematical Society 93, no. 3 (April 25, 2016): 643–63. http://dx.doi.org/10.1112/jlms/jdw010.

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19

Ren, X. "On Roth's theorem concerning a cube and three cubes of primes." Quarterly Journal of Mathematics 55, no. 3 (September 1, 2004): 357–74. http://dx.doi.org/10.1093/qmath/hah002.

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20

Philippon, Patrice. "Quelques remarques sur des questions d'approximation diophantienne." Bulletin of the Australian Mathematical Society 59, no. 2 (April 1999): 323–34. http://dx.doi.org/10.1017/s0004972700032937.

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Hoping for a hand-shake between methods from diophantine approximation theory and transcendance theory, we show how zeros estimates from transcendance theory imply Roth's type lemmas (including the product theorem). We also formulate some strong conjectures on lower bounds for linear forms in logarithms of rational numbers with rational coefficients, inspired by the subspace theorem and which would imply, for example, the abc conjecture.
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21

Wimmer, Harald K. "The matrix equation X − AXB = C and an analogue of Roth's theorem." Linear Algebra and its Applications 109 (October 1988): 145–47. http://dx.doi.org/10.1016/0024-3795(88)90204-2.

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22

Evertse, Jan-Hendrik. "An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma." Acta Arithmetica 73, no. 3 (1995): 215–48. http://dx.doi.org/10.4064/aa-73-3-215-248.

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23

Ferrante, Augusto, and Harald K. Wimmer. "Roth's similarity theorem and rank minimization in the presence of nonderogatory or semisimple eigenvalues." Linear and Multilinear Algebra 61, no. 2 (March 29, 2012): 217–31. http://dx.doi.org/10.1080/03081087.2012.672570.

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24

Ren, X. "The exceptional set in Roth's theorem concerning a cube and three cubes of primes." Quarterly Journal of Mathematics 52, no. 1 (March 1, 2001): 107–26. http://dx.doi.org/10.1093/qjmath/52.1.107.

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25

Bourgain, J. "A nonlinear version of Roth's theorem for sets of positive density in the real line." Journal d'Analyse Mathématique 50, no. 1 (December 1988): 169–81. http://dx.doi.org/10.1007/bf02796120.

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26

Endriss, Ulle. "Analysis of One-to-One Matching Mechanisms via SAT Solving: Impossibilities for Universal Axioms." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 1918–25. http://dx.doi.org/10.1609/aaai.v34i02.5561.

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We develop a powerful approach that makes modern SAT solving techniques available as a tool to support the axiomatic analysis of economic matching mechanisms. Our central result is a preservation theorem, establishing sufficient conditions under which the possibility of designing a matching mechanism meeting certain axiomatic requirements for a given number of agents carries over to all scenarios with strictly fewer agents. This allows us to obtain general results about matching by verifying claims for specific instances using a SAT solver. We use our approach to automatically derive elementary proofs for two new impossibility theorems: (i) a strong form of Roth's classical result regarding the impossibility of designing mechanisms that are both stable and strategyproof and (ii) a result establishing the impossibility of guaranteeing stability while also respecting a basic notion of cross-group fairness (so-called gender-indifference).
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27

Luckhardt, H. "Herbrand-Analysen zweier Beweise des Satzes von Roth: Polynomiale Anzahlschranken." Journal of Symbolic Logic 54, no. 1 (March 1989): 234–63. http://dx.doi.org/10.2307/2275028.

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AbstractA previously unexplored method, combining logical and mathematical elements, is shown to yield substantial numerical improvements in the area of Diophantine approximations. Kreisel illustrated the method abstractly by noting that effective bounds on the number of elements are ensured if Herbrand terms from ineffective proofs ofΣ2-finiteness theorems satisfy certain simple growth conditions. Here several efficient growth conditions for the same purpose are presented that are actually satisfied in practice, in particular, by the proofs of Roth's theorem due to Roth himself and to Esnault and Viehweg. The analysis of the former yields an exponential bound of order exp(70ε−2d2) in place of exp(285ε−2d2) given by Davenport and Roth in 1955, whereαis (real) algebraic of degreed≥ 2 and ∣α−pq−1∣ <q−2−ε. (Thus the new bound is less than the fourth root of the old one.) The new bounds extracted from the other proof arepolynomial of low degree(inε−1and logd). Corollaries: Apart from a new bound for the number of solutions of the corresponding Diophantine equations and inequalities (among them Thue's inequality), log logqν, <Cα, εν5/6+ε, whereqνare the denominators of the convergents to the continued fraction ofα.
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28

Sanders, Tom. "Roth’s theorem in ℤ4n." Analysis & PDE 2, no. 2 (May 1, 2009): 211–34. http://dx.doi.org/10.2140/apde.2009.2.211.

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29

Guralnick, Robert M. "Roth's theorems for sets of matrices." Linear Algebra and its Applications 71 (November 1985): 113–17. http://dx.doi.org/10.1016/0024-3795(85)90240-x.

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30

Green, Benjamin. "Roth’s theorem in the primes." Annals of Mathematics 161, no. 3 (May 1, 2005): 1609–36. http://dx.doi.org/10.4007/annals.2005.161.1609.

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31

Fujii, Masatoshi, and Ritsuo Nakamoto. "Rota's theorem and Heinz inequalities." Linear Algebra and its Applications 214 (January 1995): 271–75. http://dx.doi.org/10.1016/0024-3795(93)00080-j.

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32

Schoen, Tomasz, and Ilya D. Shkredov. "Roth’s theorem in many variables." Israel Journal of Mathematics 199, no. 1 (October 10, 2013): 287–308. http://dx.doi.org/10.1007/s11856-013-0049-0.

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33

Bourgain, Jean. "Roth’s theorem on progressions revisited." Journal d'Analyse Mathématique 104, no. 1 (January 2008): 155–92. http://dx.doi.org/10.1007/s11854-008-0020-x.

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34

Wimmer, H. K. "Roth's theorems for matrix equations with symmetry constraints." Linear Algebra and its Applications 199 (March 1994): 357–62. http://dx.doi.org/10.1016/0024-3795(94)90358-1.

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35

Jafarian, A. A., H. Radjavi, P. Rosenthal, and A. R. Sourour. "Simultaneous Triangularizability, Near Commutativity and Rota's Theorem." Transactions of the American Mathematical Society 347, no. 6 (June 1995): 2191. http://dx.doi.org/10.2307/2154932.

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36

LIN, MINGHUA, and HARALD K. WIMMER. "THE GENERALIZED SYLVESTER MATRIX EQUATION, RANK MINIMIZATION AND ROTH’S EQUIVALENCE THEOREM." Bulletin of the Australian Mathematical Society 84, no. 3 (July 21, 2011): 441–43. http://dx.doi.org/10.1017/s0004972711002334.

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37

BALOG, LASZLO, and VASILE BERINDE. "Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph." Carpathian Journal of Mathematics 32, no. 3 (2016): 293–302. http://dx.doi.org/10.37193/cjm.2016.03.05.

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Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T : K → X that satisfy Rothe’s boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces.
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38

Croot, Ernie, and Olof Sisask. "A new proof of Roth’s theorem on arithmetic progressions." Proceedings of the American Mathematical Society 137, no. 03 (November 4, 2008): 805–9. http://dx.doi.org/10.1090/s0002-9939-08-09594-4.

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39

Saperstein, Jeffrey. "Roth's Call it Sleep." Explicator 46, no. 1 (October 1987): 47–48. http://dx.doi.org/10.1080/00144940.1987.9935281.

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40

Farr, Cecilia K. "Roth's Call it Sleep." Explicator 46, no. 2 (January 1988): 49–51. http://dx.doi.org/10.1080/00144940.1988.9935309.

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41

McKinnon, David, and Mike Roth. "Seshadri constants, diophantine approximation, and Roth’s theorem for arbitrary varieties." Inventiones mathematicae 200, no. 2 (August 22, 2014): 513–83. http://dx.doi.org/10.1007/s00222-014-0540-1.

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42

Sanders, Tom. "Appendix to ‘Roth’s theorem on progressions revisited,’ by J. Bourgain." Journal d'Analyse Mathématique 104, no. 1 (January 2008): 193–206. http://dx.doi.org/10.1007/s11854-008-0021-9.

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43

Jafarian, A. A., H. Radjavi, P. Rosenthal, and A. R. Sourour. "Simultaneous triangularizability, near commutativity and Rota’s theorem." Transactions of the American Mathematical Society 347, no. 6 (June 1, 1995): 2191–99. http://dx.doi.org/10.1090/s0002-9947-1995-1257112-5.

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44

Roth, Fred A. "Henry Roth's Call it Sleep." Explicator 48, no. 3 (April 1990): 218–20. http://dx.doi.org/10.1080/00144940.1990.9934000.

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45

ALGHAMDI, MARYAM A., VASILE BERINDE, and NASEER SHAHZAD. "Fixed points of non-self almost contractions." Carpathian Journal of Mathematics 30, no. 1 (2014): 7–14. http://dx.doi.org/10.37193/cjm.2014.01.02.

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Let X be a convex metric space, K a non-empty closed subset of X and T : K → X a non-self almost contraction. Berinde and Pacurar [Berinde, V. and P ˘ acurar, M., Fixed point theorems for nonself single-valued almost contractions, Fixed Point Theory, 14 (2013), No. 2, 301–312], proved that if T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps ∂K (the boundary of K) into K, then T has a fixed point in K. In this paper we observe that property (M) can be removed and, hence, the above fixed point theorem takes place in a different setting.
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46

Parrish, Timothy L. "Imagining Jews in Philip Roth's "Operation Shylock"." Contemporary Literature 40, no. 4 (1999): 575. http://dx.doi.org/10.2307/1208795.

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47

Kauvar, Elaine M., and Philip Roth. "This Doubly Reflected Communication: Philip Roth's "Autobiographies"." Contemporary Literature 36, no. 3 (1995): 412. http://dx.doi.org/10.2307/1208828.

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48

Morley, C. "Bardic Aspirations: Philip Roth's Epic of America." English 57, no. 218 (January 1, 2008): 171–98. http://dx.doi.org/10.1093/english/efn017.

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49

Medin, Daniel L. "Liebliche Lüge?: Philip Roth's "Looking at Kafka"." Comparative Literature Studies 44, no. 1 (2007): 38–50. http://dx.doi.org/10.1353/cls.2007.0037.

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50

Diamant, Naomi. "Linguistic Universes in Henry Roth's "Call It Sleep"." Contemporary Literature 27, no. 3 (1986): 336. http://dx.doi.org/10.2307/1208349.

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