Distribution of values of Hecke characters of infinite order

C. S. Rajan

Acta Arithmetica (1998)

  • Volume: 85, Issue: 3, page 279-291
  • ISSN: 0065-1036

Abstract

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We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.

How to cite

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C. S. Rajan. "Distribution of values of Hecke characters of infinite order." Acta Arithmetica 85.3 (1998): 279-291. <http://eudml.org/doc/207169>.

@article{C1998,
abstract = {We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.},
author = {C. S. Rajan},
journal = {Acta Arithmetica},
keywords = {distribution of values of Hecke characters; Riemann hypothesis},
language = {eng},
number = {3},
pages = {279-291},
title = {Distribution of values of Hecke characters of infinite order},
url = {http://eudml.org/doc/207169},
volume = {85},
year = {1998},
}

TY - JOUR
AU - C. S. Rajan
TI - Distribution of values of Hecke characters of infinite order
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 3
SP - 279
EP - 291
AB - We show that the number of primes of a number field K of norm at most x, at which the local component of an idele class character of infinite order is principal, is bounded by O(x exp(-c√(log x))) as x → ∞, for some absolute constant c > 0 depending only on K.
LA - eng
KW - distribution of values of Hecke characters; Riemann hypothesis
UR - http://eudml.org/doc/207169
ER -

References

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  1. [Dav] H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, New York, 1980. 
  2. [He] E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen, Zweite Mitteilung, Math. Z. 6 (1920), 11-51; reprinted in Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959, 249-289. 
  3. [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
  4. [LO] J. Lagarias and A. M. Odlyzko, Effective versions of the Chebotarev density theorem, in: Algebraic Number Fields, A. Fröhlich (ed.), Academic Press, New York, 1977, 409-464. Zbl0362.12011
  5. [La] S. Lang, Algebraic Number Theory, Grad. Texts in Math. 110, Springer, New York, 1986. 
  6. [LT] S. Lang and H. Trotter, Frobenius Distributions in GL₂ Extensions, Lecture Notes in Math. 504, Springer, New York, 1976. 
  7. [MR] M. R. Murty and C. S. Rajan, Stronger multiplicity one theorems for forms of general type on GL₂, in: Analytic Number Theory, Proc. Conf. in Honor of Heini Halberstam, Vol. 2, B. C. Berndt, H. G. Diamond and A. J. Hildebrand (eds.), Birkhäuser, Boston, 1996, 669-683. Zbl0874.11041
  8. [VKM] V. K. Murty, Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math. 15 (1985), 535-551. Zbl0587.14009

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