Log in

Relevant bibliographies by topics / Field class / Journal articles

To see the other types of publications on this topic, follow the link: Field class.

Journal articles on the topic 'Field class'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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 'Field class.'

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

Rota, Gian-Carlo. "Class field theory." Advances in Mathematics 62, no. 1 (1986): 102. http://dx.doi.org/10.1016/0001-8708(86)90094-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Brink, James R., and Robert Gold. "Class field towers of imaginary quadratic fields." Manuscripta Mathematica 57, no. 4 (1987): 425–50. http://dx.doi.org/10.1007/bf01168670.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Zywina, David. "Explicit class field theory for global function fields." Journal of Number Theory 133, no. 3 (2013): 1062–78. http://dx.doi.org/10.1016/j.jnt.2012.02.009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Hess, Florian, and Maike Massierer. "Tame class field theory for global function fields." Journal of Number Theory 162 (May 2016): 86–115. http://dx.doi.org/10.1016/j.jnt.2015.10.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Saito, Shuji. "Class field theory for curves over local fields." Journal of Number Theory 21, no. 1 (1985): 44–80. http://dx.doi.org/10.1016/0022-314x(85)90011-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

SHPARLINSKI, IGOR E. "INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS." Glasgow Mathematical Journal 50, no. 1 (2008): 27–32. http://dx.doi.org/10.1017/s0017089507003977.

Full text

Abstract:

AbstractWe use a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field $\Q(\exp(2 \pi i/m))$ has an infinite Hilbert p-class field tower with high rank Galois groups at each step, simultaneously for all primes p of size up to about (log logm)1 + o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower over $\Q(\exp(2 \pi i/m))$ for some p≥m0.3385 + o(1). These results have immediate applications to the divisibility properties of the class number of $\Q(\exp(2 \pi i/m))$.

APA, Harvard, Vancouver, ISO, and other styles

7

Ershov, Yu L. "Local class field theory." St. Petersburg Mathematical Journal 15, no. 06 (2004): 837–47. http://dx.doi.org/10.1090/s1061-0022-04-00834-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Hoelscher, Jing Long. "Infinite class field towers." Mathematische Annalen 344, no. 4 (2009): 923–28. http://dx.doi.org/10.1007/s00208-009-0334-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Feng, Tony, Michael Harris, and Barry Mazur. "Derived class field theory." Notices of the International Consortium of Chinese Mathematicians 11, no. 2 (2023): 88–98. http://dx.doi.org/10.4310/iccm.2023.v11.n2.a10.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Gerth, Frank. "Quadratic fields with infinite Hilbert 2-class field towers." Acta Arithmetica 106, no. 2 (2003): 151–58. http://dx.doi.org/10.4064/aa106-2-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Schmidt, Bernhard. "The field descent and class groups of CM-fields." Acta Arithmetica 119, no. 3 (2005): 291–306. http://dx.doi.org/10.4064/aa119-3-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Hiranouchi, Toshiro. "Class field theory for open curves over local fields." Journal de Théorie des Nombres de Bordeaux 30, no. 2 (2018): 501–24. http://dx.doi.org/10.5802/jtnb.1036.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Cohen, Henri, and Xavier-François Roblot. "Computing the Hilbert class field of real quadratic fields." Mathematics of Computation 69, no. 231 (1999): 1229–45. http://dx.doi.org/10.1090/s0025-5718-99-01111-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

ESTES, Dennis R., and J. S. HSIA. "Spinor genera under field extensions IV: Spinor class fields." Japanese journal of mathematics. New series 16, no. 2 (1990): 341–50. http://dx.doi.org/10.4099/math1924.16.341.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Benjamin, Elliot, Franz Lemmermeyer, and C. Snyder. "Real Quadratic Fields with Abelian 2-Class Field Tower." Journal of Number Theory 73, no. 2 (1998): 182–94. http://dx.doi.org/10.1006/jnth.1998.2291.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Fesenko, Ivan B. "LOCAL CLASS FIELD THEORY: PERFECT RESIDUE FIELD CASE." Russian Academy of Sciences. Izvestiya Mathematics 43, no. 1 (1994): 65–81. http://dx.doi.org/10.1070/im1994v043n01abeh001559.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Koch, Helmut, Susanne Kukkuk, and John Labute. "Nilpotent local class field theory." Acta Arithmetica 83, no. 1 (1998): 45–64. http://dx.doi.org/10.4064/aa-83-1-45-64.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Popescu, Cristian D. "A class–field theoretical calculation." Journal de Théorie des Nombres de Bordeaux 18, no. 2 (2006): 477–86. http://dx.doi.org/10.5802/jtnb.555.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Hazewinkel, Michiel. "Book Review: Class field theory." Bulletin of the American Mathematical Society 21, no. 1 (1989): 95–102. http://dx.doi.org/10.1090/s0273-0979-1989-15772-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Gardiner, Vince, and David J. Unwin. "Computers and the field class." Journal of Geography in Higher Education 10, no. 2 (1986): 169–79. http://dx.doi.org/10.1080/03098268608708971.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Fesenko, Ivan B. "Abelian localp-class field theory." Mathematische Annalen 301, no. 1 (1995): 561–86. http://dx.doi.org/10.1007/bf01446646.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Spiess, Michael. "Class Formations and Higher Dimensional Local Class Field Theory." Journal of Number Theory 62, no. 2 (1997): 273–83. http://dx.doi.org/10.1006/jnth.1997.2048.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Gerth, Frank. "On 2-class field towers for quadratic number fields with 2-class group of type (2,2)." Glasgow Mathematical Journal 40, no. 1 (1998): 63–69. http://dx.doi.org/10.1017/s0017089500032353.

Full text

Abstract:

Let K be a quadratic number field with 2-class group of type (2,2). Thus if Sk is the Sylow 2-subgroup of the ideal class group of K, then Sk = ℤ/2ℤ × ℤ/2ℤ LetK ⊂ K1 ⊂ K2 ⊂ K3 ⊂…the 2-class field tower of K. Thus K1 is the maximal abelian unramified extension of K of degree a power of 2; K2 is the maximal abelian unramified extension of K of degree a power of 2; etc. By class field theory the Galois group Ga1 (K1/K) ≅ Sk ≅ ℤ/2ℤ × ℤ/2ℤ, and in this case it is known that Ga(K2/Kl) is a cyclic group (cf. [3] and [10]). Then by class field theory the class number of K2 is odd, and hence K2 = K3 =

APA, Harvard, Vancouver, ISO, and other styles

24

Geisser, Thomas, and Alexander Schmidt. "Tame class field theory for singular varieties over finite fields." Journal of the European Mathematical Society 19, no. 11 (2017): 3467–88. http://dx.doi.org/10.4171/jems/744.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Yoshida, Eiji. "On the 3-class field tower of some biquadratic fields." Acta Arithmetica 107, no. 4 (2003): 327–36. http://dx.doi.org/10.4064/aa107-4-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Jung, Hwanyup. "HILBERT 2-CLASS FIELD TOWERS OF IMAGINARY QUADRATIC FUNCTION FIELDS." Bulletin of the Korean Mathematical Society 50, no. 3 (2013): 1049–60. http://dx.doi.org/10.4134/bkms.2013.50.3.1049.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Lemmermeyer, Franz. "On $2$-class field towers of imaginary quadratic number fields." Journal de Théorie des Nombres de Bordeaux 6, no. 2 (1994): 261–72. http://dx.doi.org/10.5802/jtnb.114.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

CHEMS-EDDIN, Mohamed Mahmoud, Abdelkader ZEKHNINI, and Abdelmalek AZIZI. "Units and2-class field towers of some multiquadratic number fields." TURKISH JOURNAL OF MATHEMATICS 44, no. 4 (2020): 1466–83. http://dx.doi.org/10.3906/mat-2003-117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Jung, Hwanyup. "HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS." Communications of the Korean Mathematical Society 29, no. 2 (2014): 219–26. http://dx.doi.org/10.4134/ckms.2014.29.2.219.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Mouhib, A. "Infinite Hilbert 2-class field tower of quadratic number fields." Acta Arithmetica 145, no. 3 (2010): 267–72. http://dx.doi.org/10.4064/aa145-3-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Jung, Hwanyup. "HILBERT 3-CLASS FIELD TOWERS OF IMAGINARY CUBIC FUNCTION FIELDS." Journal of the Chungcheong Mathematical Society 26, no. 1 (2013): 161–66. http://dx.doi.org/10.14403/jcms.2013.26.1.161.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Jung, Hwanyup. "HILBERT 3-CLASS FIELD TOWERS OF REAL CUBIC FUNCTION FIELDS." Journal of the Chungcheong Mathematical Society 26, no. 3 (2013): 517–23. http://dx.doi.org/10.14403/jcms.2013.26.3.517.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Uzun, Mecit Kerem. "Motivic homology and class field theory over p-adic fields." Journal of Number Theory 160 (March 2016): 566–85. http://dx.doi.org/10.1016/j.jnt.2015.09.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Hiranouchi, Toshiro. "Class field theory for open curves over p-adic fields." Mathematische Zeitschrift 266, no. 1 (2009): 107–13. http://dx.doi.org/10.1007/s00209-009-0556-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Hajir, Farshid. "On the Growth ofp-Class Groups inp-Class Field Towers." Journal of Algebra 188, no. 1 (1997): 256–71. http://dx.doi.org/10.1006/jabr.1996.6849.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Halter-Koch, Franz. "A note on ray class fields of global fields." Nagoya Mathematical Journal 120 (December 1990): 61–66. http://dx.doi.org/10.1017/s002776300000324x.

Full text

Abstract:

The notion of a ray class field, which is fundamental in Takagi’s class field theory, has no immediate analogon in the function field case. The reason for this lies in the lacking of a distinguished maximal order. In this paper I overcome this difficulty by a relative version of the notion of ray class fields to be defined for every holomorphy ring of the field. The prototype for this new notion is M. Rosen’s definition of a Hilbert class field for function fields [6].

APA, Harvard, Vancouver, ISO, and other styles

37

Benjamin, Elliot. "Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields." Bulletin of the Australian Mathematical Society 48, no. 3 (1993): 379–83. http://dx.doi.org/10.1017/s0004972700015835.

Full text

Abstract:

Letkbe an imaginary quadratic number field and letk1be the 2-Hilbert class field ofk. IfCk,2, the 2-Sylow subgroup of the ideal class group ofk, is elementary and |Ck,2|≥ 8, we show thatCk1,2is not cyclic. IfCk,2is isomorphic toZ/2Z×Z/4ZandCk1,2is elementary we show thatkhas finite 2-class field tower of length at most 2.

APA, Harvard, Vancouver, ISO, and other styles

38

JOSHI, KIRTI, and CAMERON MCLEMAN. "INFINITE HILBERT CLASS FIELD TOWERS FROM GALOIS REPRESENTATIONS." International Journal of Number Theory 07, no. 01 (2011): 1–8. http://dx.doi.org/10.1142/s1793042111003879.

Full text

Abstract:

We investigate class field towers of number fields obtained as fixed fields of modular representations of the absolute Galois group of the rational numbers. First, for each k ∈ {12, 16, 18, 20, 22, 26}, we give explicit rational primes ℓ such that the fixed field of the mod-ℓ representation attached to the unique normalized cusp eigenform of weight k on SL2(ℤ) has an infinite class field tower. Further, under a conjecture of Hardy and Littlewood, we prove the existence of infinitely many cyclotomic fields of prime conductor, providing infinitely many such primes ℓ for each k in the list. Final

APA, Harvard, Vancouver, ISO, and other styles

39

Azizi, Abdelmalek, Mohammed Rezzougui, Mohammed Taous, and Abdelkader Zekhnini. "On the Hilbert 2-class field of some quadratic number fields." International Journal of Number Theory 15, no. 04 (2019): 807–24. http://dx.doi.org/10.1142/s179304211950043x.

Full text

Abstract:

In this paper, we investigate the cyclicity of the [Formula: see text]-class group of the first Hilbert [Formula: see text]-class field of some quadratic number field whose discriminant is not a sum of two squares. For this, let [Formula: see text] be different prime integers. Put [Formula: see text], and denote by [Formula: see text] its [Formula: see text]-class group and by [Formula: see text] (respectively [Formula: see text]) its first (respectively second) Hilbert [Formula: see text]-class field. Then, we are interested in studying the metacyclicity of [Formula: see text] and the cyclici

APA, Harvard, Vancouver, ISO, and other styles

40

DA ROCHA, R., and W. A. RODRIGUES. "WHERE ARE ELKO SPINOR FIELDS IN LOUNESTO SPINOR FIELD CLASSIFICATION?" Modern Physics Letters A 21, no. 01 (2006): 65–74. http://dx.doi.org/10.1142/s0217732306018482.

Full text

Abstract:

This paper proves that from the algebraic point of view ELKO spinor fields belong together with Majorana spinor fields to a wider class, the so-called flagpole spinor fields, corresponding to the class 5, according to Lounesto spinor field classification. We show moreover that algebraic constraints imply that any class 5 spinor field is such that the 2-component spinor fields entering its structure have opposite helicities. The proof of our statement is based on Lounesto general classification of all spinor fields, according to the relations and values taken by their associated bilinear covari

APA, Harvard, Vancouver, ISO, and other styles

41

Alkam, Osama, and Mehpare Bilhan. "Class number of (v, n, M)-extensions." Bulletin of the Australian Mathematical Society 63, no. 1 (2001): 21–34. http://dx.doi.org/10.1017/s0004972700019080.

Full text

Abstract:

An analogue of cyclotomic number fields for function fields over the finite field q, was investigated by L. Carlitz in 1935 and has been studied recently by D. Hayes, M. Rosen, S. Galovich and others. For each nonzero polynomial M in q [T], we denote by k (ΛM) the cyclotomic function field associated with M, where k = q(T). Replacing T by 1/T in k and considering the cyclotomic function field Fv that corresponds to (1/T)v+1 gets us an extension of k, denoted by Lv, which is the fixed field of Fv modulo . We define a (v, n, M)-extension to be the composite N = knk (Λm) Lv where kn is the con

APA, Harvard, Vancouver, ISO, and other styles

42

Kim, Junhyeung, Hisatoshi Kodani, and Masanori Morishita. "Nilpotent class field theory for manifolds." Proceedings of the Japan Academy, Series A, Mathematical Sciences 89, no. 1 (2013): 15–19. http://dx.doi.org/10.3792/pjaa.89.15.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Stevenhagen, Peter. "Unramified class field theory for orders." Transactions of the American Mathematical Society 311, no. 2 (1989): 483. http://dx.doi.org/10.1090/s0002-9947-1989-0978366-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

KERZ, MORITZ, and YIGENG ZHAO. "HIGHER IDELES AND CLASS FIELD THEORY." Nagoya Mathematical Journal 236 (October 2, 2018): 214–50. http://dx.doi.org/10.1017/nmj.2018.34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Belolipetsky, Mikhail, and Alexander Lubotzky. "Manifolds counting and class field towers." Advances in Mathematics 229, no. 6 (2012): 3123–46. http://dx.doi.org/10.1016/j.aim.2012.02.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Stewart, Scott E. "Field behavior oftripedalia cystophora(class cubozoa)." Marine and Freshwater Behaviour and Physiology 27, no. 2-3 (1996): 175–88. http://dx.doi.org/10.1080/10236249609378963.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Azizi, Abdelmalek, and Mohammed Talbi. "Galois group for some class field." Miskolc Mathematical Notes 15, no. 2 (2014): 317. http://dx.doi.org/10.18514/mmn.2014.723.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Iovita, Adrian, and Alexandru Zaharescu. "Nondiscrete local ramified class field theory." Journal of Mathematics of Kyoto University 35, no. 2 (1995): 325–39. http://dx.doi.org/10.1215/kjm/1250518774.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Titan, Qingchun. "Class Field Theory for Arithmetic Surfaces." K-Theory 13, no. 2 (1998): 123–49. http://dx.doi.org/10.1023/a:1007722903192.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Wiesend, Götz. "Class field theory for arithmetic schemes." Mathematische Zeitschrift 256, no. 4 (2007): 717–29. http://dx.doi.org/10.1007/s00209-006-0095-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

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!