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Relevant bibliographies by topics / Kummer's theorem

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Academic literature on the topic 'Kummer's theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Kummer's theorem"

1

Milovanovic, Gradimir, Rakesh Parmar, and Arjun Rathie. "A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1." Applicable Analysis and Discrete Mathematics 12, no. 1 (2018): 257–72. http://dx.doi.org/10.2298/aadm171017002m.

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Motivated by recent generalizations of classical theorems for the series 2F1 [Integral Transform. Spec. Funct. 229(11), (2011), 823-840] and interesting Laplace transforms of Kummer's confluent hypergeometric functions obtained by Kim et al. [Math. Comput. Modelling 55 (2012), 1068-1071], first we express generalized summations theorems in explicit forms and then by employing these, we derive various new and useful Laplace transforms of convolution type integrals by using product theorem of the Laplace transforms for a pair of Kummer's confluent hypergeometric function.

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Rakha, Medhat A., Mohamed M. Awad, and Arjun K. Rathie. "On an Extension of Kummer's Second Theorem." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/128458.

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The aim of this paper is to establish an extension of Kummer's second theorem in the form e-x/2F22[a,2+d;x2a+2,d;]=F10[-;x2/16a+3/2;]+((a/d-1/2)/(a+1))x F10[-;x2/16a+3/2;]+(cx2/2(2a+3))F10[-;x2/16a+5/2;], where c=1/a+11/2-a/d+a/d(d+1), d≠0,-1,-2,…. Ford=2a, we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminatingF23(2)series. The results derived in this paper are simple, interesting, and easily established and may be useful in ph

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Ball, Tyler, Tom Edgar, and Daniel Juda. "Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem." Mathematics Magazine 87, no. 2 (2014): 135–43. http://dx.doi.org/10.4169/math.mag.87.2.135.

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Harizanov, Valentina, Martin Kummer, and Jim Owings. "Frequency computations and the cardinality theorem." Journal of Symbolic Logic 57, no. 2 (1992): 682–87. http://dx.doi.org/10.2307/2275300.

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In 1960 G. F. Rose [R] made the following definition: A function f: ω → ω is (m, n)-computable, where 1 ≤ m ≤ n, iff there exists a recursive function R: ωn → ωn such that, for all n-tuples (x1,…, xn) of distinct natural numbers,J. Myhill (see [McN, p. 393]) asked if f had to be recursive if m was close to n; B. A. Trakhtenbrot [T] responded by showing in 1963 that f is recursive whenever 2m > n. This result is optimal, because, for example, the characteristic function of any semirecursive set is (1,2)-computable. Trakhtenbrot's work was extended by E. B. Kinber [Ki1], using similar techniq

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5

Qureshi, M. I., M. Sadiq Khan, M. A. Pathan, and N. U. Khan. "Some multivariable Gaussian hypergeometric extensions of the Preece theorem." ANZIAM Journal 48, no. 1 (2006): 143–50. http://dx.doi.org/10.1017/s1446181100003473.

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AbstractSome generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric function and Srivastava's quadruple hypergeometric function F(4) and triple hypergeometric function F(3). Some known results of Preece, Pathan and Bailey are also obtained as special cases.

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Kim, Yong-Sup, and Arjun K. Rathie. "APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES2F1." Bulletin of the Korean Mathematical Society 46, no. 6 (2009): 1201–11. http://dx.doi.org/10.4134/bkms.2009.46.6.1201.

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Sands, Jonathan W. "Kummer's and Iwasawa's Version of Leopoldt's Conjecture." Canadian Mathematical Bulletin 31, no. 3 (1988): 338–46. http://dx.doi.org/10.4153/cmb-1988-049-0.

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AbstractWe present a refinement of Iwasawa's approach to Leopoldt's conjecture on the non-vanishing of the p-adic regulator of an algebraic number field K. As an application, the conjecture for K implies the conjecture for a solvable extension L of degree g over K if g is relatively prime to p — 1 and p does not divide g, the discriminant of K, and the quotient of class numbers where is a primitive pth root of unity. This can be viewed as generalizing a theorem of Kummer on cyclotomic units.

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Ainkooran, Deepa, Mohamed M. Awad, and Medhat A. Rakha. "Another Method for Deriving two Results Contiguous to Kummer's Second Theorem." Journal of Interpolation and Approximation in Scientific Computing 2013 (2013): 1–6. http://dx.doi.org/10.5899/2013/jiasc-00030.

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Baider, Alberto, and Richard Churchill. "Uniqueness and non-uniqueness of normal forms for vector fields." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 108, no. 1-2 (1988): 27–33. http://dx.doi.org/10.1017/s0308210500026482.

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SynopsisThe use of normal forms in the study of equilibria of vector fields and Hamiltonian systems is a well-established practice and is described in standard references (e.g. [1], [7] or [10]). Also well known is the fact that such normal forms are not unique, and the relationship between distinct normal forms of the same vector field has also been investigated, in particular by M. Kummer [8] and A. Brjuno [2,3] (also see [12]). In this paper we use this relationship to extract invariants of the vector field directly from an arbitrary normal form. The treatment is sufficiently general to han

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Kouba, Omran. "Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action." Journal of Classical Analysis, no. 2 (2016): 79–88. http://dx.doi.org/10.7153/jca-09-09.

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Dissertations / Theses on the topic "Kummer's theorem"

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Pescim, Rodrigo Rossetto. "The new class of Kummer beta generalized distributions: theory and applications." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-30012014-112231/.

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In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as

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2

Jha, Vijay. "The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem /." Kingston, Ont., Canada : Queen's University, 1993. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=005385035&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Tari, Kévin. "Automorphismes des variétés de Kummer généralisées." Thesis, Poitiers, 2015. http://www.theses.fr/2015POIT2301/document.

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Dans ce travail, nous classifions les automorphismes non-symplectiques des variétés équivalentes par déformations à des variétés de Kummer généralisées de dimension 4, ayant une action d'ordre premier sur le réseau de Beauville-Bogomolov. Dans un premier temps, nous donnons les lieux fixes des automorphismes naturels de cette forme. Par la suite, nous développons des outils sur les réseaux en vue de les appliquer à nos variétés. Une étude réticulaire des tores complexes de dimension 2 permet de mieux comprendre les automorphismes naturels sur les variétés de type Kummer. Nous classifions final

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4

Hamza, Marwa. "Caractérisations des familles exponentielles naturelles cubiques : étude des lois Beta généralisées et de certaines lois de Kummer." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0036/document.

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Cette thèse contient deux parties différentes. Dans la première partie, nous nous sommes intéressés aux familles exponentielles naturelles cubiques dont la fonction variance est un polynôme de degré inférieur ou égal à 3. Nous donnons trois caractérisations de ces familles en se basant sur une approche Bayesienne. L’une de ces caractérisations repose sur le fait que la fonction cumulante vérifie une équation différentielle. La deuxième partie de notre travail est consacrée aux conséquences de la propriété d’indépendance de type « Matsumoto-Yor » qui a été développée par Koudou et Vallois. Cett

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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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<p>This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions

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Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g<=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la r

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Michalik, Jindřich. "Kombinatorické posloupnosti čísel a dělitelnost." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-373204.

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This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1

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8

莊子平. "Explicit Class Field Theory for Kummer Extensions." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/685d2x.

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碩士<br>國立臺灣師範大學<br>數學系<br>96<br>In this thesis, we first introduce some known results. Then we define a pairing and use the known results to discuss properties of this pairing. Finally, we use this pairing to discuss local class field theory for Kummer extension without employing the classical local class field theory.

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9

Li, Anly, and 李安莉. "On Kummer theory of division points over Drinfeld modules." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/66939229486118463838.

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博士<br>國立清華大學<br>數學系<br>87<br>Let k be the rational function field, and A be the polynomial ring. Let ψ be a Drinfeld module over a finite extension L of k which is viewed as an A-field of generic characteristic. Via ψ, L becomes an A-module. We denote this module by ψ(L). Denote Λ(M,ψ) to be the module of M-torsion points of ψ. For finitely generated A-submodule Γof ψ(L), set H(Γ,M) to be the Galois group Gal(L(Λ(M,ψ),1/MΓ)/L(Λ(M,ψ) )). In this thesis, we establish the Kummer theory of division points over the Carlitz module, Drinfeld modules of rank one, singular Drinfeld modules

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Books on the topic "Kummer's theorem"

1

Jha, Vijay. The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem. Queen's University, 1993.

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2

Kummer, Ernst Eduard. Der Briefwechsel zwischen Kummer und Reuschle: Ein Beitrag zur Geschichte der algebraischen Zahlentheorie. Rauner, 2006.

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3

Boniface, Jacqueline. A process of generalization. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.18.

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This article examines Ernst Kummer’s creation of ideal factors, which provides an interesting example of generalization within the set of complex numbers. Kummer developed a theory of ideal numbers in order to generalize arithmetical properties of natural numbers by extending these properties to certain complex numbers. His goal was to make complex numbers analogous to natural ones. This article first considers Kummer’s use of several analogies, primarily with arithmetic and chemistry, to come up with ideal factors of complex numbers. It then situates Kummer’s investigations on complex numbers

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Book chapters on the topic "Kummer's theorem"

1

Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Theorem of Clausen and von Staudt, and Kummer’s Congruence." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_3.

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2

Hoyt, William L. "Elliptic fiberings of Kummer surfaces." In Number Theory. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0083572.

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Cohn, Harvey. "Humbert’s Conic Model and the Kummer Surface." In Number Theory. Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4419-9060-0_7.

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Shiga, Hironori. "Appendix: Periods on the Kummer surface." In Algebra and Number Theory. Hindustan Book Agency, 2005. http://dx.doi.org/10.1007/978-93-86279-23-1_24.

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Cohen, Henri. "Computing Defining Polynomials Using Kummer Theory." In Advanced Topics in Computional Number Theory. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8489-0_5.

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Gunaratne, H. Sunil. "A New Generalisation of the Kummer Congruence." In Computational Algebra and Number Theory. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-1108-1_18.

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Venkov, Alexei B. "Automorphic Functions and the Kummer Problem." In Spectral Theory of Automorphic Functions and Its Applications. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1892-4_10.

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Hilbert, David. "Norm Residues and Non-residues of a Kummer Field." In The Theory of Algebraic Number Fields. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03545-0_29.

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Hilbert, David. "Ambig Ideal Classes and Genera in Regular Kummer Fields." In The Theory of Algebraic Number Fields. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03545-0_32.

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Hilbert, David. "The Number of Genera in a Regular Kummer Field." In The Theory of Algebraic Number Fields. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03545-0_34.

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Conference papers on the topic "Kummer's theorem"

1

Georgieva-Grosse, Mariana Nikolova, and Georgi Nikolov Georgiev. "Contribution to the theory of the complex Kummer function." In 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2014. http://dx.doi.org/10.1109/iceaa.2014.6903882.

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2

Favaro, Alberto. "Electromagnetic wave propagation in metamaterials: A visual guide to Fresnel-Kummer surfaces and their singular points." In 2016 URSI International Symposium on Electromagnetic Theory (EMTS). IEEE, 2016. http://dx.doi.org/10.1109/ursi-emts.2016.7571473.

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Georgiev, Georgi Nikolov, and Mariana Nikolova Georgieva-Grosse. "Some zeros of the real Kummer function and their application to the theory of waveguides." In 2016 Progress in Electromagnetic Research Symposium (PIERS). IEEE, 2016. http://dx.doi.org/10.1109/piers.2016.7735279.

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