Distribution of values of Hecke characters of infinite order

• Autorzy: C. S. Rajan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11M41: Other Dirichlet series and zeta functions
• 11N99: None of the above, but in this section
• 11R45: Density theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 3
• Strony: 279-291

Daty

wydano

1998

otrzymano

1997-08-19

poprawiono

1998-01-27

Twórcy

autor

C. S. Rajan

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India

Bibliografia

• [Dav] H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, New York, 1980.
• [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.
• [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
• [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.
• [La] S. Lang, Algebraic Number Theory, Grad. Texts in Math. 110, Springer, New York, 1986.
• [LT] S. Lang and H. Trotter, Frobenius Distributions in GL₂ Extensions, Lecture Notes in Math. 504, Springer, New York, 1976.
• [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.
• [VKM] V. K. Murty, Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math. 15 (1985), 535-551.