Skip to main content
SpringerLink
Log in

Some problems of effectivity in arithmetic, geometry and analysis

  • Conference paper
  • First Online:
Number Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1052))

  • 585 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérique 18, Soc. Math. de France, 1974.

    Google Scholar 

  2. K. Chandrasekharan, Arithmetical Functions, Grundlehren series Vol. 167, Springer-Verlag, 1970.

    Google Scholar 

  3. S. D. Cohen, The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc.

    Google Scholar 

  4. P. Deligne, Les constantes des équations fonctionnelles des fonctions L. Lecture Notes in Math. 349(1972), 501–597.

    Article  MathSciNet  Google Scholar 

  5. _____, Les constantes de équations fonctionnelles, Séminaire Delange-Pisot-Poitou 1969/70.

    Google Scholar 

  6. _____, Valeurs de fonctions L et périodes d'intégrales, Proc. Symposia in Pure Math. Vol. 33(1979), Part 2, 313–346.

    Article  MathSciNet  Google Scholar 

  7. _____, La conjecture de Weil, II, Publ. Math. Vol. 52, IHES (1980), 137–252.

    Article  MathSciNet  MATH  Google Scholar 

  8. V. G. Drinfeld, Langlands' conjecture for GL(2) over functional fields, Proc. International Congress of Math. 2(1978), 565–574.

    MathSciNet  Google Scholar 

  9. P. X. Gallagher, A large sieve estimate near σ = 1, Invent. Math. 11(1970), 329–339.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Godement and H. Jacquet, Zeta functions of simple algebras, Lecture Notes in Math. Vol. 260, Springer-Verlag 1972.

    Google Scholar 

  11. H. Jacquet and J. Shalika, On euler products and the classification of automorphic representations I, Amer. J. Math. 103(1981), 449–558.

    MathSciNet  MATH  Google Scholar 

  12. _____, On Euler products and the classification theory of automorphic forms II, Amer. J. Math. 103(1981), 777–815.

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Jacquet, I. P. Shapiro and J. Shalika, Rankin-Selberg convolutions, preprint.

    Google Scholar 

  14. _____, Conductor of generic representations of the general linear group, C. R. Acad. Sci., Paris, 5. 292, Series I (1981), 611–616.

    MATH  Google Scholar 

  15. J. Lagarias, H. Montgomery and A. Odlyzko, A bound for the least prime ideal in the Chebotarev density theorem, Invent. Math. 54 (1979), 277–296.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. P. Langlands, Problems in the theory of automorphic forms, Lecture Notes in Math. Vol. 170, Springer-Verlag (1970), 18–86.

    Article  MathSciNet  MATH  Google Scholar 

  17. C. J. Moreno, Advanced analytic number theory, Part I: Ramification theoretic methods, Contemporary Math. Vol. 15, AMS (1983).

    Google Scholar 

  18. _____, Advanced analytic number theory, Part II: L-functions, (in preparation).

    Google Scholar 

  19. _____, An effective Chebotarev density theory, (preprint, University of Illinois 1975).

    Google Scholar 

  20. C. J. Moreno, An analytic proof of the multiplicity one theorem, (preprint).

    Google Scholar 

  21. _____, Explicit formulas in the theory of automorphic forms, Lecture Notes in Math., Vol. 626, Springer-Verlag (1976), 73–216.

    Article  MathSciNet  Google Scholar 

  22. A. Ogg, Abelian curves of 2-power conductor, Proc. Camb. Phil. Soc. 62(1966), 143–148.

    Article  MathSciNet  MATH  Google Scholar 

  23. _____, On a convolution of L-series, Invent. Math. 7(1969), 297–312.

    Article  MathSciNet  MATH  Google Scholar 

  24. A. N. Parshin, Quelques Conjectures de finitude en géométrie diophantienne, International Congress of Math. 1970, 467–471.

    Google Scholar 

  25. _____, Minimal models of curves of genus 2 and homomorphisms of abelian varieties defined over a field of finite characteristic, Math. USSR Izvestija 6(1972), No. 1 65–108.

    Article  MATH  Google Scholar 

  26. _____, Algebraic curves over function fields, Soviet Math. Dokl. 9(1968), No. 6., 1419–1422.

    MATH  Google Scholar 

  27. _____, Algebraic curves over function fields, I, Math. USSR Izvestija, 2(1968), No. 2, 1145–1170.

    Article  MathSciNet  MATH  Google Scholar 

  28. J.-P. Serre, Quelques applications du théorème de densité de Chebotarev, Publ. Math. IHES 54(1981), 123–202.

    Article  MATH  Google Scholar 

  29. _____, Abelian l-adic Representations and Elliptic Curves, New York, Benjamin Publishing Co., 1968.

    MATH  Google Scholar 

  30. _____, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15(1972), 259–331.

    Article  MathSciNet  Google Scholar 

  31. _____, Représentations l-adiques, Algebraic number theory, International Symposium, Kyoto (1977), 177–193.

    Google Scholar 

  32. _____, Letter to Szpiro (March 18, 1982).

    Google Scholar 

  33. I. R. Shafarevitch, Algebraic number fields, International Congress of Math. 1962, 163–176 (= A.M.S. Transl. Ser. 2, Vol. 31, 25–39).

    Google Scholar 

  34. I. R. Shafarevitch and J. Tate, The rank of elliptic curves, Soviet Math. Dokl. 8(1967), No. 4, 916–920.

    Google Scholar 

  35. J. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harper and Row, New York, 1965, pp. 93–110.

    MATH  Google Scholar 

  36. _____, On the conjectures of Birch and Swinnerton-Dyer and a geometric analogue, Sém. Bourbaki, 1965/66, exposé 306.

    Google Scholar 

  37. H. Yoshida, Abelian varieties with complex multiplications and representations of the Weil groups, Ann. Math. 114(1981), 87–102.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 61801, Urbana, Illinois, U.S.A.

    Carlos J. Moreno

Authors
  1. Carlos J. Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David V. Chudnovsky Gregory V. Chudnovsky Harvey Cohn Melvin B. Nathanson

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Moreno, C.J. (1984). Some problems of effectivity in arithmetic, geometry and analysis. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071545

Download citation

  • DOI: https://doi.org/10.1007/BFb0071545

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12909-7

  • Online ISBN: 978-3-540-38788-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation