Representation of prime powers in arithmetical progressions by binary quadratic forms

Franz Halter-Koch

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 141-149
  • ISSN: 1246-7405

Abstract

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Let Γ be a set of binary quadratic forms of the same discriminant, Δ a set of arithmetical progressions and m a positive integer. We investigate the representability of prime powers p m lying in some progression from Δ by some form from Γ .

How to cite

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Halter-Koch, Franz. "Representation of prime powers in arithmetical progressions by binary quadratic forms." Journal de théorie des nombres de Bordeaux 15.1 (2003): 141-149. <http://eudml.org/doc/249085>.

@article{Halter2003,
abstract = {Let $\Gamma $ be a set of binary quadratic forms of the same discriminant, $\Delta $ a set of arithmetical progressions and $m$ a positive integer. We investigate the representability of prime powers $p^m$ lying in some progression from $\Delta $ by some form from $\Gamma $.},
author = {Halter-Koch, Franz},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {arithmetic progressions; genus theory; quadratic forms},
language = {eng},
number = {1},
pages = {141-149},
publisher = {Université Bordeaux I},
title = {Representation of prime powers in arithmetical progressions by binary quadratic forms},
url = {http://eudml.org/doc/249085},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Halter-Koch, Franz
TI - Representation of prime powers in arithmetical progressions by binary quadratic forms
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 141
EP - 149
AB - Let $\Gamma $ be a set of binary quadratic forms of the same discriminant, $\Delta $ a set of arithmetical progressions and $m$ a positive integer. We investigate the representability of prime powers $p^m$ lying in some progression from $\Delta $ by some form from $\Gamma $.
LA - eng
KW - arithmetic progressions; genus theory; quadratic forms
UR - http://eudml.org/doc/249085
ER -

References

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  1. [1] H. Cohn, A Classical Invitation to Algebraic Numbers and Class Fields. Springer, 1978. Zbl0395.12001MR506156
  2. [2] D.A. Cox, Primes of the form x2 + ny2. J. Wiley, 1989. Zbl0701.11001MR1028322
  3. [3] F. Halter-Koch, Representation of primes by binary quadratic forms of discriminant -256q and -128q. Glasgow Math. J.35 (1993), 261-268. Zbl0783.11018MR1220569
  4. [4] F. Halter-Koch, A Theorem of Ramanujan Concerning Binary Quadratic Forms. J. Number Theory44 (1993), 209-213. Zbl0784.11011MR1225953
  5. [5] F. Halter-Koch, Geschlechtertheorie der Ringklassenkörpers. J. Reine Angew. Math.250 (1971), 107-108. Zbl0236.12004MR292797
  6. [6] H. Hasse, Number Theory. Springer, 1980. Zbl0423.12002MR562104
  7. [7] P. Kaplan, K.S. Williams, Representation of Primes in Arithmetic Progressions by Binary Quadratic Forms. J. Number Theory45 (1993), 61-67. Zbl0790.11031MR1239546
  8. [8] T. Kusaba, Remarque sur la distribution des nombres premiers. C. R. Acad. Sci. Paris Sér. A265 (1967), 405-407. Zbl0204.06604MR224574
  9. [9] A. Meyer, Über einen Satz von Dirichlet. J. Reine Angew. Math.103 (1888), 98-117. JFM20.0192.02

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