The Hooley-Huxley contour method for problems in number fields III : frobenian functions

Mark D. Coleman

Journal de théorie des nombres de Bordeaux (2001)

  • Volume: 13, Issue: 1, page 65-76
  • ISSN: 1246-7405

Abstract

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In this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to “small regions”. Special cases concern Ramanujan's tau function in small intervals and relative norms in “small regions” of elements from a full module of the Galois extension.

How to cite

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Coleman, Mark D.. "The Hooley-Huxley contour method for problems in number fields III : frobenian functions." Journal de théorie des nombres de Bordeaux 13.1 (2001): 65-76. <http://eudml.org/doc/248729>.

@article{Coleman2001,
abstract = {In this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to “small regions”. Special cases concern Ramanujan's tau function in small intervals and relative norms in “small regions” of elements from a full module of the Galois extension.},
author = {Coleman, Mark D.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Frobenius multiplicative functions; asymptotic expressions},
language = {eng},
number = {1},
pages = {65-76},
publisher = {Université Bordeaux I},
title = {The Hooley-Huxley contour method for problems in number fields III : frobenian functions},
url = {http://eudml.org/doc/248729},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Coleman, Mark D.
TI - The Hooley-Huxley contour method for problems in number fields III : frobenian functions
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 65
EP - 76
AB - In this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to “small regions”. Special cases concern Ramanujan's tau function in small intervals and relative norms in “small regions” of elements from a full module of the Galois extension.
LA - eng
KW - Frobenius multiplicative functions; asymptotic expressions
UR - http://eudml.org/doc/248729
ER -

References

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  1. [1] M.D. Coleman, The Hooley-Huxley contour method for problems in number fields I: Arithmetic Functions. J. Number Theory74, (1999), 250-277. Zbl0978.11052MR1671657
  2. [2] M.D. Coleman, The Hooley-Huxley contour method for problems in number fields II: Factorization and Divisiblity. Submitted to J. Number Theory. Zbl1066.11049
  3. [3] P. Deligne, J.-P. Serre, Formes modulaires de poids 1. Ann. scient. Ec. Norm. Sup. (4) 7 (1974), 507-530. Zbl0321.10026MR379379
  4. [4] R.W.K. Odoni, On the norms of algebraic integers. Mathematika22 (1975), 71-80. Zbl0313.12007MR424757
  5. [5] R.W.K. Odoni, Representations of algebraic integers by binary quadratic forms and norm forms of full modules of extension fields. J. Number Theory10 (1978), 324-333. Zbl0411.12010MR506642
  6. [6] R.W.K. Odoni, The distribution of integral and prime-integral values of systems of full-norm polynomials and affine-decomposable polynomials. Mathematika26 (1979), 80-87. Zbl0444.12008MR557130
  7. [7] R.W.K. Odoni, Notes on the method of Frobenian functions, with applications to the coefficents of modular forms. In: Elementary and analytic theory of numbers, Banach Center Publications, vol. 17, Polish Scientific Publishers, Warsaw1985, pp. 371-403. Zbl0596.10040MR840484
  8. [8] R.W.K. Odoni, On the distribution of norms of ideals in given ray-classes and the theory of central ray-class fields. Acta Arith.52 (1989), 373-397. Zbl0694.12007MR1030089
  9. [9] K. Ramachandra, Some problems of analytic number theory. Acta Arith.31 (1976), 313-324. Zbl0291.10034MR424723

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