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Journal articles on the topic 'Numberd Theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

C.S., Harisha. "Graph Theory Approach to Number Theory Theorems." Journal of Advanced Research in Dynamical and Control Systems 12, no. 01-Special Issue (2020): 568–72. http://dx.doi.org/10.5373/jardcs/v12sp1/20201105.

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2

Maslov, V. P. "Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics." Russian Journal of Mathematical Physics 23, no. 4 (2016): 510–28. http://dx.doi.org/10.1134/s1061920816040075.

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3

Steele, G. Ander. "Carmichael numbers in number rings." Journal of Number Theory 128, no. 4 (2008): 910–17. http://dx.doi.org/10.1016/j.jnt.2007.08.009.

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4

Quadling, Douglas, Bob Burn, and Amanda Chetwynd. "A Cascade of Numbers: An Introduction to Number Theory." Mathematical Gazette 81, no. 491 (1997): 329. http://dx.doi.org/10.2307/3619238.

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5

Shiu, P., and Paulo Ribenboim. "My Numbers, My Friends. Popular Lectures on Number Theory." Mathematical Gazette 85, no. 504 (2001): 540. http://dx.doi.org/10.2307/3621797.

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6

Marshall, John U. "The Löschian Numbers As a Problem in Number Theory." Geographical Analysis 7, no. 4 (2010): 421–26. http://dx.doi.org/10.1111/j.1538-4632.1975.tb01054.x.

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7

Stakhov, A. "The “Golden” Number Theory and New Properties of Natural Numbers." British Journal of Mathematics & Computer Science 11, no. 6 (2015): 1–15. http://dx.doi.org/10.9734/bjmcs/2015/21385.

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8

Timberlake, Todd. "Random numbers and random matrices: Quantum chaos meets number theory." American Journal of Physics 74, no. 6 (2006): 547–53. http://dx.doi.org/10.1119/1.2198883.

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9

Daileda, Ryan C., Raju Krishnamoorthy, and Anton Malyshev. "Maximal class numbers of CM number fields." Journal of Number Theory 130, no. 4 (2010): 936–43. http://dx.doi.org/10.1016/j.jnt.2009.09.013.

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10

De Koninck, J. M., N. Doyon, and I. Kátai. "Counting the number of twin Niven numbers." Ramanujan Journal 17, no. 1 (2008): 89–105. http://dx.doi.org/10.1007/s11139-008-9127-z.

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11

Fellows, Michael R., Serge Gaspers, and Frances A. Rosamond. "Parameterizing by the Number of Numbers." Theory of Computing Systems 50, no. 4 (2011): 675–93. http://dx.doi.org/10.1007/s00224-011-9367-y.

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12

Perucca, Antonella, and Pietro Sgobba. "Kummer theory for number fields and the reductions of algebraic numbers." International Journal of Number Theory 15, no. 08 (2019): 1617–33. http://dx.doi.org/10.1142/s179304211950091x.

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For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and torsion-free multiplicative subgroup of a number field [Formula: see text] having rank [Formula: see text], then the ratio between [Formula: see text] and the Kummer degree [Formula: see text] is bounded independently of [Formula: see text]. We then apply this result to generalize to higher rank a theorem of Ziegler from 2006 about the multiplicative

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13

Lefevre, Adam. "Number Theory." Grand Street, no. 59 (1997): 99. http://dx.doi.org/10.2307/25008125.

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14

Scourfield, E. J. "NUMBER THEORY." Bulletin of the London Mathematical Society 17, no. 1 (1985): 93–94. http://dx.doi.org/10.1112/blms/17.1.93.

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15

Balasubramanian, K. "Number Theory." Journal of Mathematical Chemistry 36, no. 2 (2004): 167. http://dx.doi.org/10.1023/b:jomc.0000038791.72217.20.

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16

Schroeder, M. R. "Number theory." IEEE Potentials 8, no. 3 (1989): 14–17. http://dx.doi.org/10.1109/45.41531.

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17

Perucca, Antonella, and Pietro Sgobba. "Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II." Uniform distribution theory 15, no. 1 (2020): 75–92. http://dx.doi.org/10.2478/udt-2020-0004.

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AbstractLet K be a number field, and let G be a finitely generated and torsion-free subgroup of K×. For almost all primes p of K, we consider the order of the cyclic group (G mod 𝔭), and ask whether this number lies in a given arithmetic progression. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if ℓe is a prime power and a is a multiple of ℓ (and a is a multiple of 4 if ℓ =2), then the density of primes 𝔭 of K such th

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18

Xavier, G. Britto Antony, V. Chandrasekar, and S. Gokulakrishnan. "Generalized Stirling numbers of third kind and its applications in number theory." International Journal of Mathematical Analysis 9 (2015): 897–906. http://dx.doi.org/10.12988/ijma.2015.5383.

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19

Zazkis, Rina, and Jeffrey Truman. "From Trigonometry to Number Theory… and Back: Extending LCM to Rational Numbers." Digital Experiences in Mathematics Education 1, no. 1 (2015): 79–86. http://dx.doi.org/10.1007/s40751-015-0001-5.

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20

Agarwal, Ravi P. "Pythagoreans Figurative Numbers: The Beginning of Number Theory and Summation of Series." Journal of Applied Mathematics and Physics 09, no. 08 (2021): 2038–113. http://dx.doi.org/10.4236/jamp.2021.98132.

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21

Chang, Ku-Young, and Soun-Hi Kwon. "The imaginary abelian number fields with class numbers equal to their genus class numbers." Journal de Théorie des Nombres de Bordeaux 12, no. 2 (2000): 349–65. http://dx.doi.org/10.5802/jtnb.283.

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22

Gómez-Torrente, Mario. "On the Essence and Identity of Numbers." THEORIA. An International Journal for Theory, History and Foundations of Science 30, no. 3 (2015): 317–29. http://dx.doi.org/10.1387/theoria.14099.

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Taking as premises some intuitions about the essences of natural numbers, pluralities and sets, the paper offers an argument that the natural numbers could not be the “Zermelo numbers”, the “Von Neumann numbers”, the “Kripke numbers”, or the “positions in the ω-structure”, among other things. The argument’s conclusion is thus Benacerrafian in form, but it is emphasized that the argument is anti-Benacerrafian in substance, as it is perfectly compatible and in fact congenial with some views on which the numbers could be things of certain other kinds.

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23

Daileda, Ryan C. "Non-abelian number fields with very large class numbers." Acta Arithmetica 125, no. 3 (2006): 215–55. http://dx.doi.org/10.4064/aa125-3-2.

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24

Banerjee, Soumyarup, Manav Batavia, Ben Kane, et al. "Fermat's polygonal number theorem for repeated generalized polygonal numbers." Journal of Number Theory 220 (March 2021): 163–81. http://dx.doi.org/10.1016/j.jnt.2020.05.024.

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25

Liu, Peide, Sepehr Hendiani, Morteza Bagherpour, Seyed Farid Ghannadpour, and Amin Mahmoudi. "Utility-Numbers Theory." IEEE Access 7 (2019): 56994–7008. http://dx.doi.org/10.1109/access.2019.2912922.

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26

Ehrlich, Philip. "Number systems with simplicity hierarchies: a generalization of Conway's theory of surreal numbers." Journal of Symbolic Logic 66, no. 3 (2001): 1231–58. http://dx.doi.org/10.2307/2695104.

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Introduction. In his monograph On Numbers and Games [7], J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many other numbers including ω, ω, /2, 1/ω, and ω − π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered “number” fields—be individually definable in terms of sets of von Neumann-Bernays-Gödel set theory with Global Choice, henceforth NBG [cf. 21, Ch. 4], it may be said to contain “All Numbers Great

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27

Brüdern, Jörg, Hugh Montgomery, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 10, no. 4 (2013): 2963–3037. http://dx.doi.org/10.4171/owr/2013/51.

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28

Brüdern, Jörg, Hugh Montgomery, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 13, no. 4 (2017): 2975–3030. http://dx.doi.org/10.4171/owr/2016/53.

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29

Brüdern, Jörg, Kaisa Matomäki, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 16, no. 4 (2020): 3141–205. http://dx.doi.org/10.4171/owr/2019/50.

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30

Bowen, Alan C. "Boethian Number Theory." Ancient Philosophy 9, no. 1 (1989): 137–43. http://dx.doi.org/10.5840/ancientphil19899136.

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31

Shiu, P., Gareth A. Jones, and J. Mary Jones. "Elementary Number Theory." Mathematical Gazette 82, no. 495 (1998): 534. http://dx.doi.org/10.2307/3619931.

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32

Blackmore, G. W., I. N. Stewart, and D. O. Tall. "Algebraic Number Theory." Mathematical Gazette 73, no. 463 (1989): 65. http://dx.doi.org/10.2307/3618234.

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33

Grosswald, Emil, Charles Vanden Eynden, and Kenneth H. Rosen. "Elementary Number Theory." American Mathematical Monthly 96, no. 5 (1989): 460. http://dx.doi.org/10.2307/2325169.

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34

Snapp, Bart, and Chris Snapp. "Automotive Number Theory." Math Horizons 17, no. 1 (2009): 26–27. http://dx.doi.org/10.1080/10724117.2009.11974839.

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35

Snapp, Bart, and Chris Snapp. "Automotive Number Theory." Math Horizons 17, no. 1 (2009): 26–27. http://dx.doi.org/10.4169/194762109x468328.

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36

Iwaniec, Henryk. "Automorphic Number Theory." Current Developments in Mathematics 2003, no. 1 (2003): 35–52. http://dx.doi.org/10.4310/cdm.2003.v2003.n1.a2.

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37

Tokuo, Kenji. "Quantum Number Theory." International Journal of Theoretical Physics 43, no. 12 (2004): 2461–81. http://dx.doi.org/10.1007/s10773-004-7711-6.

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38

Kim, Kwang-Seob, and John C. Miller. "Class numbers of large degree nonabelian number fields." Mathematics of Computation 88, no. 316 (2018): 973–81. http://dx.doi.org/10.1090/mcom/3335.

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39

Rajasekaran, Aayush, Jeffrey Shallit, and Tim Smith. "Additive Number Theory via Automata Theory." Theory of Computing Systems 64, no. 3 (2019): 542–67. http://dx.doi.org/10.1007/s00224-019-09929-9.

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40

EHRLICH, PHILIP, and ELLIOT KAPLAN. "NUMBER SYSTEMS WITH SIMPLICITY HIERARCHIES: A GENERALIZATION OF CONWAY’S THEORY OF SURREAL NUMBERS II." Journal of Symbolic Logic 83, no. 2 (2018): 617–33. http://dx.doi.org/10.1017/jsl.2017.9.

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AbstractIn [16], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field ${\bf{No}}$ of surreal numbers was brought to the fore and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to an initial subfield of ${\bf{No}}$, i.e., a subfield of ${\bf{No}}$ that is an initial subtree of ${\bf{No}}$. In this sequel to [16], analogous results for ordered abelian groups and ordered domains are established which in turn are employed to characterize the convex subgroups and convex subdomains of initial subfields of ${\bf

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41

Byeon, Dongho. "Class Numbers and Iwasawa Invariants of Certain Totally Real Number Fields." Journal of Number Theory 79, no. 2 (1999): 249–57. http://dx.doi.org/10.1006/jnth.1999.2433.

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42

Wagner, Stephan G. "Numbers with fixed sum of digits in linear recurrent number systems." Ramanujan Journal 14, no. 1 (2006): 43–68. http://dx.doi.org/10.1007/s11139-006-0001-6.

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43

PETERSEN, KATHLEEN L., and CHRISTOPHER D. SINCLAIR. "EQUIDISTRIBUTION OF ALGEBRAIC NUMBERS OF NORM ONE IN QUADRATIC NUMBER FIELDS." International Journal of Number Theory 07, no. 07 (2011): 1841–61. http://dx.doi.org/10.1142/s1793042111004666.

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Given a fixed quadratic extension K of ℚ, we consider the distribution of elements in K of norm one (denoted [Formula: see text]). When K is an imaginary quadratic extension, [Formula: see text] is naturally embedded in the unit circle in ℂ and we show that it is equidistributed with respect to inclusion as ordered by the absolute Weil height. By Hilbert's Theorem 90, an element in [Formula: see text] can be written as [Formula: see text] for some [Formula: see text], which yields another ordering of [Formula: see text] given by the minimal norm of the associated algebraic integers. When K is

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44

Boyd, David W., Karma Dajani, and Cor Kraaikamp. "Ergodic Theory of Numbers." American Mathematical Monthly 111, no. 7 (2004): 633. http://dx.doi.org/10.2307/4145181.

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45

Williams, Patricia J., and Ruth Colker. "Theory by the Numbers." Women's Review of Books 12, no. 9 (1995): 9. http://dx.doi.org/10.2307/4022086.

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46

Nadler, Sam B. "Continuum Theory and Graph Theory: Disconnection Numbers." Journal of the London Mathematical Society s2-47, no. 1 (1993): 167–81. http://dx.doi.org/10.1112/jlms/s2-47.1.167.

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47

Gode, Deepak Bhalchandra. "Complex Number Theory without Imaginary Number (i)." OALib 01, no. 07 (2014): 1–13. http://dx.doi.org/10.4236/oalib.1100856.

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48

Bergelson, Vitaly, Nikos Frantzikinakis, Terence Tao, and Tamar Ziegler. "Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory." Oberwolfach Reports 9, no. 4 (2012): 2985–3059. http://dx.doi.org/10.4171/owr/2012/50.

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49

Ammari, Habib, Liliana Borcea, Thorsten Hohage, and Barbara Kaltenbacher. "Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory." Oberwolfach Reports 9, no. 4 (2012): 3061–127. http://dx.doi.org/10.4171/owr/2012/51.

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50

Volovich, Igor V. "Number theory as the ultimate physical theory." P-Adic Numbers, Ultrametric Analysis, and Applications 2, no. 1 (2010): 77–87. http://dx.doi.org/10.1134/s2070046610010061.

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