Northcott's theorem on heights II. The quadratic case

Wolfgang M. Schmidt

Acta Arithmetica (1995)

  • Volume: 70, Issue: 4, page 343-375
  • ISSN: 0065-1036

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Wolfgang M. Schmidt. "Northcott's theorem on heights II. The quadratic case." Acta Arithmetica 70.4 (1995): 343-375. <http://eudml.org/doc/206755>.

@article{WolfgangM1995,
author = {Wolfgang M. Schmidt},
journal = {Acta Arithmetica},
keywords = {heights; number of decomposable quadratic forms; asymptotic formulas; Dirichlet's asymptotic formula; ideals; quadratic case of Schanuel's asymptotic formula; number of points in projective space},
language = {eng},
number = {4},
pages = {343-375},
title = {Northcott's theorem on heights II. The quadratic case},
url = {http://eudml.org/doc/206755},
volume = {70},
year = {1995},
}

TY - JOUR
AU - Wolfgang M. Schmidt
TI - Northcott's theorem on heights II. The quadratic case
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 4
SP - 343
EP - 375
LA - eng
KW - heights; number of decomposable quadratic forms; asymptotic formulas; Dirichlet's asymptotic formula; ideals; quadratic case of Schanuel's asymptotic formula; number of points in projective space
UR - http://eudml.org/doc/206755
ER -

References

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  1. [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, 1976. 
  2. [2] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, 1959. Zbl0086.26203
  3. [3] H. Davenport, On a principle of Lipschitz, J. London Math. Soc. 26 (1951), 179-183. Zbl0042.27504
  4. [4] D. Goldfeld and J. Hoffstein, Eisenstein series of 1/2-integral weight and the mean value of real Dirichlet L-series, Invent. Math. 80 (1985), 185-208. Zbl0564.10043
  5. [5] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Clarendon Press, Oxford, 1954. Zbl0058.03301
  6. [6] E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Chelsea, 1948. 
  7. [7] Y. R. Katznelson, Asymptotics for singular integral matrices in convex domains and applications, Ph.D. Dissertation, Stanford Univ., 1991. 
  8. [8] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
  9. [9] R. Lipschitz, Sitzungsber. Akad. Berlin, 1865, 174-185. 
  10. [10] D. G. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc. 45 (1949), 502-509 and 510-518. Zbl0035.30701
  11. [11] S. H. Schanuel, Heights in number fields, Bull. Soc. Math. France 107 (1979), 433-449. Zbl0428.12009
  12. [12] W. M. Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, 1991. 
  13. [13] W. M. Schmidt, Northcott's theorem on heights, I. A general estimate, Monatsh. Math. 115 (1993), 169-181. Zbl0784.11054
  14. [14] J.-P. Serre, Lectures on the Mordell-Weil Theorem, Vieweg, Braunschweig, 1988. 
  15. [15] C. L. Siegel, The average measure of quadratic forms with given determinant and signature, Ann. of Math. 45 (1944), 667-685. Zbl0063.07007
  16. [16] C. L. Siegel, Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. 1969, 71-86. Zbl0186.36703
  17. [17] C. L. Siegel, Lectures on the Geometry of Numbers, rewritten by K. Chandrasekharan, Springer, 1988. 
  18. [18] J. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), 395-403. Zbl0579.14035

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