Relevant bibliographies by topics / Artin’s conjecture

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Artin’s conjecture'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Artin’s conjecture"

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Foote, Richard. "Nonmonomial characters and Artin’s conjecture." Transactions of the American Mathematical Society 321, no. 1 (January 1, 1990): 261–72. http://dx.doi.org/10.1090/s0002-9947-1990-0987161-9.

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Virdol, Cristian. "Artin’s conjecture for abelian varieties." Kyoto Journal of Mathematics 56, no. 4 (December 2016): 737–43. http://dx.doi.org/10.1215/21562261-3664896.

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Murty, M. Ram. "Artin’s conjecture for primitive roots." Mathematical Intelligencer 10, no. 4 (September 1988): 59–67. http://dx.doi.org/10.1007/bf03023749.

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Martin, Kimball. "A symplectic case of Artin’s Conjecture." Mathematical Research Letters 10, no. 4 (2003): 483–92. http://dx.doi.org/10.4310/mrl.2003.v10.n4.a7.

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Virdol, Cristian. "On Artin’s conjecture for CM elliptic curves." Kyoto Journal of Mathematics 60, no. 4 (December 2020): 1361–71. http://dx.doi.org/10.1215/21562261-2019-0064.

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Brüdern, Jörg, and Olivier Robert. "On Artin’s conjecture: Linear slices of diagonal hypersurfaces." Transactions of the American Mathematical Society 372, no. 3 (May 9, 2019): 1867–911. http://dx.doi.org/10.1090/tran/7635.

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Pappalardi, Francesco, and Andrea Susa. "An analogue of Artin’s conjecture for multiplicative subgroups of the rationals." Archiv der Mathematik 101, no. 4 (October 2013): 319–30. http://dx.doi.org/10.1007/s00013-013-0563-7.

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Gee, Toby, and Payman Kassaei. "Companion forms in parallel weight one." Compositio Mathematica 149, no. 6 (May 10, 2013): 903–13. http://dx.doi.org/10.1112/s0010437x12000875.

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AbstractLet $p\gt 2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a $\mathrm{mod} \hspace{0.167em} p$ Galois representation to arise from a $\mathrm{mod} \hspace{0.167em} p$ Hilbert modular form of parallel weight one, by proving a ‘companion forms’ theorem in this case. The techniques used are a mixture of modularity lifting theorems and geometric methods. As an application, we show that Serre’s conjecture for $F$ implies Artin’s conjecture for totally odd two-dimensional representations over $F$.
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Zoeteman, M. "Uniformly counting primes with a given primitive root and in an arithmetic progression." International Journal of Number Theory 15, no. 10 (November 2019): 2115–34. http://dx.doi.org/10.1142/s1793042119501161.

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We study the number of primes with a given primitive root and in an arithmetic progression under the assumption of a suitable form of the generalized Riemann Hypothesis. Previous work of Lenstra, Moree and Stevenhagen has given asymptotics without an explicit error term, we provide an explicit error term by combining their work with the method of Hooley regarding Artin’s primitive root conjecture. We give an application to a Diophantine problem involving primes with a given primitive root.
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ZHU, HONGWEI, and MINJIA SHI. "ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES." Bulletin of the Australian Mathematical Society 98, no. 1 (April 29, 2018): 159–66. http://dx.doi.org/10.1017/s0004972718000175.

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We study linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$ when $q$ is an odd prime power. When $q^{\unicode[STIX]{x1D6FF}}+1$ is divisible by $n$, we obtain an exact count of linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$. For certain values of $n$ and $q$ and assuming Artin’s conjecture for primitive roots, we show that the relative distance of these codes satisfies a modified Gilbert–Varshamov bound.
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Dissertations / Theses on the topic "Artin’s conjecture"

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Celis, Cerón M. A. "Conjectura de Artin para pares de formas aditivas de grau 6." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4090.

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Celis Cerón, Mónica Andrea. Artin’s conjecture for pairs of additive sextic forms. Goiânia, 2014. 62p. MSc. Dissertation. Instituto de Matemática e Estatística, Universidade Federal de Goiás. Consider the system of equations a1xk1+ a2xk2+ + asxks= 0; b1xk1+ b2xk2+ + bsxks= 0; where a1; a2; ; as; b1; b2; ; bs 2 Z A special case of Artin’s conjecture states that the above system must have nontrivial solutions in every p-adic field, Qp, provided only that s 2k2+ 1. In this text we show that the conjecture is true when k = 6.
Celis Cerón, Mónica Andrea. Conjectura de Artin para pares de formas aditivas de grau 6. Goiânia, 2014. 62p. Dissertação de Mestrado. Instituto de Matemática e Estatística, Universidade Federal de Goiás. Consideremos o sistema de equações a1xk1+ a2xk2+...+ asxks= 0; b1xk1+ b2xk2+ + bsxks= 0; onde, a 1; a 2; ; as; b1; b2; ; bs 2 Z. Um caso especial da conjectura de Artin nos diz que o sistema anterior tem solução não trivial em todo corpo p-ádico, Qp, sempre que s 2k2+ 1. Neste trabalho mostraremos que a conjectura é válida quando k = 6.
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Ferreira, Alaídes Inácio Stival. "Condições de solubilidade p-ádica de pares de formas diagonais e alguns casos especiais." Universidade Federal de Goiás, 2009. http://repositorio.bc.ufg.br/tede/handle/tde/2890.

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This text is above solvability in systems of two forms additive over p-adics fields: with of degree k and variables n > 4k at lesat p > 3k4 ; with of degree an k odd integer at least n > 6k+1 variables; and with of degree 5 and p > 101 for n ≥ 31 variables, and for all p with n ≥ 36 variables, with the possible exceptions of p = 5 and p = 11.
Este texto é sobre solubilidade no corpo dos p-ádicos de sistemas de duas formas aditivas: com grau k e variáveis n > 4k apartir de p > 3k4 ; com grau k ímpar apartir de n > 6k +1 variáveis; e de grau 5 com p > 101 para n ≥ 31 variáveis, e para todo p com n ≥ 36 variáveis, com exceções de p = 5 e p = 11.
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Lelis, Jean Carlos Aguiar. "Uma confirmação da conjectura de Artin para pares de formas diagonais de graus 2 e 3." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/5567.

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In this work we present some methods used in the study of systems of additive forms on local fields, and a proof for a particular case of Artin’s Conjecture, which says that every systems with R additive forms of degrees k1; :::;kR has non trivial p-adic solution for any prime p, if the number s of variables is higher than k2 1 +k2 2 + +k2R, given by Wooley [12], where he shows that G(3;2) = 11. Keywords
Nesse trabalho, nós apresentamos alguns dos métodos usados no estudo de formas aditivas sobre corpos locais, e uma prova para um caso particular da Conjectura de Artin, que afirma que todo sistema de R formas aditivas de graus k1;k2; :::;kR possui solução p-ádica não trivial para todo p primo, se o número s de variáveis for maior que k2 1 +k2 2 + +k2R , dada por Wooley [12], onde ele mostra que G(3;2) = 11.
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Pappalardi, Francesco. "On Artin's conjecture for primitive roots." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41128.

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Various generalizations of the Artin's Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform version of the Chebotarev Density Theorem for the field ${ cal Q}( zeta sb{l},2 sp{1/l})$ valid for the range $l < { rm log} x$ is proven. A uniform asymptotic formula for the number of primes up to x for which there exists a primitive root less than s is established. Lower bounds for the exponent of the class group of imaginary quadratic fields valid for density one sets of discriminants are determined.
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Kaesberg, Miriam Sophie [Verfasser]. "Two Cases of Artin's Conjecture / Miriam Sophie Kaesberg." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2021. http://d-nb.info/1228364958/34.

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Camacho, Adriana Marcela Fonce. "Conjectura de Artin: um estudo sobre pares de formas aditivas." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/5326.

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This work is based mainly on the Brunder and Godinho article [2] which shows proof of the conjecture of Artin methods using p-adic, although the conjecture is stated on the real numbers which makes the proof is show an equivalence on the field of the number p-adic method with the help of colored variables ya contraction of variables so as to prove the statement, taking the first level and ensuring a nontrivial solution in the following levels.
Este trabalho é baseado principalmente no artigo de Brunder e Godinho [2] o qual mostra a prova da conjetura de Artin usando métodos p-ádicos, ainda que a conjetura se afirma sobre o números reais o que faz a prova é mostrar uma equivalência sobre o corpo dos número p-ádicos com ajuda do método de variáveis coloridas e a contração de variáveis para assim provar a afirmação, tomando o primeiro nível e assim garantindo uma solução não trivial nos níveis seguintes.
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Souza, Neto Tertuliano Carneiro de. "Pares de formas aditivas e a conjectura de Artin." reponame:Repositório Institucional da UnB, 2011. http://repositorio.unb.br/handle/10482/8840.

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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2011.
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Seja f(x1, ..., xn) = a1xk 1 + ... + anxk n g(x1, ..., xn) = b1xk 1 + ... + bnxk n (1) um par de formas aditivas de grau pΤ (p − 1). Estamos interessados em obter condições que garantam a existência de zeros p-ádicos para o par (1). Uma conhecida conjectura, devida a Emil Artin, afirma que a condição n > 2k2 é suficiente. Utilizando técnicas da Teoria Combinatória dos Números, provamos que a condição n > 2 p (p/ P – 1) k2 − 2k é suficiente se k = 2.3Τ ou 4.5Τ, e em qualquer caso se Τ≥ (p – 1)/ 2. _____________________________________________________________________________________ ABSTRACT
Let f(x1, ..., xn) = a1xk 1 + ... + anxk n g(x1, ..., xn) = b1xk 1 + ... + bnxk n (1) be a pair of additive forms of degree pΤ (p − 1). We are interested in finding conditions which guarantee the existence of p-adic zeros to the pair (2). A well-known conjecture due to Emil Artin states that the condition n > 2k2 is sufficient. By means of techniques of Combinatorial Number Theory, we prove that n > 2 p (p/ P – 1) k2 − 2k is sufficient if k = 2.3Τ ou 4.5Τ, and in any case if Τ≥ (p – 1)/ 2.
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Ambrose, Christopher Daniel [Verfasser], Valentin [Akademischer Betreuer] Blomer, and Preda [Akademischer Betreuer] Mihăilescu. "On Artin's primitive root conjecture / Christopher Daniel Ambrose. Gutachter: Valentin Blomer ; Preda Mihailescu. Betreuer: Valentin Blomer." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2014. http://d-nb.info/1054191484/34.

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Veras, Daiane Soares. "Formas aditivas sobre corpos p-ádicos." reponame:Repositório Institucional da UnB, 2017. http://repositorio.unb.br/handle/10482/24228.

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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2017.
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Davenport e Lewis provaram uma versão da Conjectura de Artin que diz que, denotando por Γ* (k , p) o menor número de variáveis para o qual uma forma aditiva com coeficientes inteiros e grau k possui solução p−ádica não trivial, onde p é um número primo, então Γ* (k , p) ≤ k 2 +1 e a igualdade acontece quando p = k+1. Sabe-se que, em geral, quando k + 1 é composto essa cota é suficiente, mas não é necessária. Nessa tese melhoramos a cota dada pela conjectura e obtemos o número exato de variáveis necessárias para garantir a solubilidade p-ádica não trivial de uma forma aditiva de grau k com coeficientes inteiros, sempre que p − 1 divide k. Mais precisamente, escrevendo k = γq + r onde γ depende do grau k e0 ≤ r ≤ γ − 1, provamos que Γ* (k , p)≤( p γ−1) q+ p r , e a igualdade vale para os primos p tais que p − 1 divide k. Como aplicação desse resultado, mostramos que, se k = 54, então 1049 variáveis são suficientes para garantir a solubilidade p-ádica não trivial para todo p. Para k = 24, M. P. Knapp mostrou que são necessárias 289 variáveis para garantir a solubilidade p-ádica não trivial para todo p, entretanto, ainda como aplicação do resultado citado acima, provamos que, se p ≠ 13, então 140 variáveis são suficientes para garantir a solubilidade desejada. Além disso, encontramos o valor exato de Γ* (10 , p) para cada p primo.
Davenport and Lewis have proved a version of Artin’s Conjecture wich states that, denoting by Γ* (k , p) the least number of variables for wich an additive form with integer coefficients and degree k has a nontrivial p-adic solution, where p is a prime number, then Γ* (k , p)≤ k 2 +1 and the equality occurs when p = k + 1. It is known that in general when k + 1 is composite this bound is sufficient but it is not necessary. In this work we improve the conjecture´s bound and give the exact number of necessary variables to states that an additive form with integers coefficients and degree k has a nontrivial p-adic solution, since p − 1 divide k. More precisely, writing k = γq + r with γ depending of degree k and 0 ≤ r ≤ γ − 1, then Γ* (k , p)≤ ( p γ−1) q+ p r , and the equality occurs when p − 1 divide k. As an application of this result we show that, if k = 54, then 1049 variables are sufficient to ensure the nontrivial p-adic solubility for all p. For k = 24, M. P. Knapp has proved that 289 variables are necessary to ensure the nontrivial p-adic solution for all p, however, still as an application of the previous result, we show that, if p ≠ 13, then 140 variables are sufficient to ensure de solubility desired. Moreover, we give the exact value to Γ* (10, p ) for each prime p.
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Dejou, Gaëlle. "Conjecture de brumer-stark non abélienne." Phd thesis, Université Claude Bernard - Lyon I, 2011. http://tel.archives-ouvertes.fr/tel-00618624.

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La recherche d'annulateurs du groupe des classes d'idéaux d'une extension abélienne de Q est un sujet classique et remonte à des travaux de Kummer et Stickelberger. La conjecture de Brumer-Stark porte sur les extensions abéliennes de corps de nombres et prédit qu'un élément de l'anneau de groupe du groupe de Galois, appelé élément de Brumer-Stickelberger, est un annulateur du groupe des classes de l'extension. De plus, elle stipule que les générateurs des idéaux principaux obtenus possèdent des propriétés bien particulières. Cette thèse est dédiée à la généralisation de cette conjecture aux extensions de corps de nombres galoisiennes mais non abéliennes. Dans un premier temps, nous nous focalisons sur l'étude de l'analogue non abélien de l'élément de Brumer, nécessaire à l'établissement d'une conjecture non abélienne. La seconde partie est consacrée à l'énoncé de la conjecture de Brumer-Stark non abélienne et à ses reformulations, ainsi qu'aux propriétés qu'elle vérifie. Nous nous intéressons notamment aux propriétés de changement d'extension. Nous étudions ensuite le cas spécifique des extensions dont le groupe de Galois possède un sous-groupe abélien H distingué d'indice premier. Sous la validité de la conjecture de Brumer-Stark associée à certaines extensions abéliennes, nous en déduisons deux résultats suivant la parité du cardinal de H : dans le cas impair, nous démontrons la conjecture de Brumer-Stark non abélienne, et dans le cas pair, nous établissons un résultat d'abélianité permettant d'obtenir, sous des hypothèses supplémentaires, la conjecture non abélienne. Enfin nous effectuons des vérifications numériques de la conjecture non abélienne permettant de démontrer cette conjecture dans les exemples testés.
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Books on the topic "Artin’s conjecture"

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Basmaji, Jacques, Ian Kiming, Martin Kinzelbach, Xiangdong Wang, and Loïc Merel. On Artin's Conjecture for Odd 2-dimensional Representations. Edited by Gerhard Frey. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074106.

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1944-, Frey Gerhard, ed. On Artin's conjecture for odd 2-dimensional representations. Berlin: Springer-Verlag, 1994.

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Ekelund, Robert B., John D. Jackson, and Robert D. Tollison. The Impact of Death and Bubbles in American Art. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190657895.003.0007.

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Chapter 7 presents a dissection of two important issues affecting the art market and the fate of artists: “a death effect” and “bubbles.” Death of an artist is a guarantee that additional legitimate output will not be forthcoming, the “Coase durable monopoly conjecture.” Evidence indicates that the price path of seventeen artists who died over the sample period rises as the artist approaches death. After death, price may rise or fall with supply and demand, but we find it rises for our contemporary artists. “Bubbles”—rapid price increases—have and do occur in the art market. We find that art price behavior parallel GDP prior to 2008, but rose much faster thereafter. This result, coupled with an increasingly skewed world income distribution and billionaire buying, potentially denotes an “art price bubble.”
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Marcaccio, Fabian, Katy Siegel, Christiane Meyer-Stoll, Thomas Keenan, and Greg Lynn. Fabian Marcaccio: 661 Conjectures For A New Paint Management 1989-2004. Walther Konig, 2005.

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Book chapters on the topic "Artin’s conjecture"

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Rosen, Michael. "Artin’s Primitive Root Conjecture." In Graduate Texts in Mathematics, 149–67. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6046-0_10.

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Ram Murty, M. "Artin’s Conjecture for Primitive Roots." In Mathematical Conversations, 113–27. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0195-0_11.

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Prasad, Dipendra, and C. S. Yogananda. "A Report on Artin’s Holomorphy Conjecture." In Number Theory, 301–14. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-7023-8_16.

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Prasad, Dipendra, and C. S. Yogananda. "A Report on Artin’s Holomorphy Conjecture." In Number Theory, 301–14. Gurgaon: Hindustan Book Agency, 2000. http://dx.doi.org/10.1007/978-93-86279-02-6_16.

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Jensen, Erik, and M. Ram Murty. "Artin’s Conjecture for Polynomials Over Finite Fields." In Number Theory, 167–81. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-7023-8_10.

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Jensen, Erik, and M. Ram Murty. "Artin’s Conjecture for Polynomials Over Finite Fields." In Number Theory, 167–81. Gurgaon: Hindustan Book Agency, 2000. http://dx.doi.org/10.1007/978-93-86279-02-6_10.

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Murty, M., and Kathleen Petersen. "The generalized Artin conjecture and arithmetic orbifolds." In CRM Proceedings and Lecture Notes, 259–65. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/crmp/047/17.

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Paris, Luis. "Lectures on Artin Groups and the $$K(\pi ,1)$$ Conjecture." In Groups of Exceptional Type, Coxeter Groups and Related Geometries, 239–57. New Delhi: Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-1814-2_13.

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Kiming, Ian, and Xiangdong Wang. "Examples of 2-dimensional, odd galois representations of A5-type over ℚ satisfying the Artin conjecture." In Lecture Notes in Mathematics, 109–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074112.

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Kiming, Ian. "On the experimental verification of the artin conjecture for 2-dimensional odd galois representations over Q liftings of 2-dimensional projective galois representations over Q." In Lecture Notes in Mathematics, 1–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074107.

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Conference papers on the topic "Artin’s conjecture"

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Heath-Brown, D. R. "Artin's Conjecture on Zeros of p-adic Forms." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0049.

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Hashimoto, Ryūta, and Takao Komatsu. "Certain integers related to Ankeny-Artin-Chowla conjecture." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841895.

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You might also be interested in the extended bibliographies on the topic 'Artin’s conjecture' for particular source types:
Journal articles Dissertations / Theses
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