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A Report on Artin’s Holomorphy Conjecture

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Abstract

The purpose of this paper is to present a report on the current status of Artin’s holomorphy conjecture. For a fascinating account of how Artin was led to defining his L-series and his ‘reciprocity law’ see [19].

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References

  1. E. Artin, Über die Zetafunktionen gewisser algebraischer Zahlkörper, Math. Ann. 89 (1923), 147–156.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Artin, Über eine neue Art von L-reihen, Hamb. Abh. (1923), 89–108.

    Google Scholar 

  3. E. Artin, Beweis des allgemeinen Reziprozitätsgesetzes, Hamb. Abh. 5 (1927), 353–363.

    Article  MATH  Google Scholar 

  4. E. Artin, Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren, Hamb. Abh. 8 (1930), 292–306.

    Article  MATH  Google Scholar 

  5. R. Brauer, On the zeta functions of algebraic number fields, Amer. J. Math. 69 (1947), 243–250.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Brauer, On Artin’s L-series with general group characters, Ann. of Math. 48 (1947), 502–514.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Buhler, Icosahedral Galois Representations, Lecture Notes in Mathematics 654 Springer-Verlag, 1978.

    Google Scholar 

  8. K. Buzzard and Taylor, R., Companion forms and weight one forms, preprint, 1997.

    Google Scholar 

  9. W. Duke, The dimension of the space of cusp forms of weight one, International Math. Res. Notices, No. 2, (1995), 99–109.

    Article  MathSciNet  Google Scholar 

  10. G. Frey, On Artin’s Conjecture for Odd 2-Dimensional Representations, Lecture Notes in Mathematics 1585 Springer-Verlag, 1994.

    Google Scholar 

  11. R. Foote and Murty, V.K., Zeros and poles of Artin L-series, Math. Proc. Camb. Phil. Soc. (1989), 105,5,5–11.

    Google Scholar 

  12. E. Hecke, Über eine neue Anwendung dur Zetafunktion auf die Arithmetik der Zahlkörper, Göttinger Nachrichten (1917), 90–95.

    Google Scholar 

  13. C. Khare, Remarks on mod p forms of weight 1, International Math. Research Notices (1997), No. 3, 127–133.

    Article  MathSciNet  Google Scholar 

  14. G.O. Michler, On Artin L-series of irreducible characters of the symmetric group S n, Algebra and Number Theory, Ed.: G. Frey and J. Ritter, Walter de Gruyter (1994), 153–163.

    Google Scholar 

  15. M. Ram Murty, A motivated introduction to the Langlands’ Programme, Advances in Number Theory, Ed.: F. Gouvea and N. Yui, Clarendon Press, Oxford (1993), 37–66.

    Google Scholar 

  16. J.-P. Serre, Modular forms of weight one and Galois representations, in: Algebraic Number Theory,edited by Frohlich, Academic Press, 193–268.

    Google Scholar 

  17. H. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23 (1974), 135–152.

    Article  MathSciNet  MATH  Google Scholar 

  18. N.I. Shephered-Barron and Taylor, R., Mod 2 and Mod 5 icosahedral representations, Journal of the AMS, volume 10 (1997), 283–298.

    Google Scholar 

  19. J. Tate, The general reciprocity law, Mathematical developments arising from Hilbert Problems, volume 27 (AMSPSPM series), 1976. Ed.: F.E. Browder, 311–322.

    Google Scholar 

  20. J. Tate, Les conjetures de Stark sur les Fonctions L d’Artin en s = 0, Progress in Mathematics vol. 47 Birkhauser, 1984.

    Google Scholar 

  21. R. Taylor, Icosahedral Galois Representations, Olga Taussky-Todd: in memoriam. Pacific Journal of Mathematics (1997), 337–347.

    Google Scholar 

  22. K. Uchida, On Artin’s L-functions, Tohoku Math. J. 27 (1975), 75–81.

    Article  MathSciNet  MATH  Google Scholar 

  23. R.W. van der Waal, On a conjecture of Dedekind on zeta functions, Indag. Math. 37 (1975), 83–86.

    Google Scholar 

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© 2000 Hindustan Book Agency (India) and Indian National Science Academy

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Prasad, D., Yogananda, C.S. (2000). A Report on Artin’s Holomorphy Conjecture. In: Bambah, R.P., Dumir, V.C., Hans-Gill, R.J. (eds) Number Theory. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7023-8_16

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  • DOI: https://doi.org/10.1007/978-3-0348-7023-8_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7025-2

  • Online ISBN: 978-3-0348-7023-8

  • eBook Packages: Springer Book Archive

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