Representation of prime powers in arithmetical progressions by binary quadratic forms
Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 141-149.

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.

Soit Γ une famille de formes quadratiques à deux variables de même discriminant, Δ un ensemble de progressions arithmétiques et m un entier strictement positif. Nous nous intéressons au problème de la représentation des puissances de nombres premiers p m appartenant à une progression de Δ par une forme quadratique de Γ.

@article{JTNB_2003__15_1_141_0,
     author = {Franz Halter-Koch},
     title = {Representation of prime powers in arithmetical progressions by binary quadratic forms},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {141--149},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     doi = {10.5802/jtnb.393},
     zbl = {1048.11030},
     mrnumber = {2019007},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.393/}
}
TY  - JOUR
TI  - Representation of prime powers in arithmetical progressions by binary quadratic forms
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2003
DA  - 2003///
SP  - 141
EP  - 149
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.393/
UR  - https://zbmath.org/?q=an%3A1048.11030
UR  - https://www.ams.org/mathscinet-getitem?mr=2019007
UR  - https://doi.org/10.5802/jtnb.393
DO  - 10.5802/jtnb.393
LA  - en
ID  - JTNB_2003__15_1_141_0
ER  - 
%0 Journal Article
%T Representation of prime powers in arithmetical progressions by binary quadratic forms
%J Journal de Théorie des Nombres de Bordeaux
%D 2003
%P 141-149
%V 15
%N 1
%I Université Bordeaux I
%U https://doi.org/10.5802/jtnb.393
%R 10.5802/jtnb.393
%G en
%F JTNB_2003__15_1_141_0
Franz Halter-Koch. Representation of prime powers in arithmetical progressions by binary quadratic forms. Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 141-149. doi : 10.5802/jtnb.393. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.393/

[1] H. Cohn, A Classical Invitation to Algebraic Numbers and Class Fields. Springer, 1978. | MR

[2] D.A. Cox, Primes of the form x2 + ny2. J. Wiley, 1989. | MR | Zbl

[3] F. Halter-Koch, Representation of primes by binary quadratic forms of discriminant -256q and -128q. Glasgow Math. J. 35 (1993), 261-268. | MR | Zbl

[4] F. Halter-Koch, A Theorem of Ramanujan Concerning Binary Quadratic Forms. J. Number Theory 44 (1993), 209-213. | MR | Zbl

[5] F. Halter-Koch, Geschlechtertheorie der Ringklassenkörpers. J. Reine Angew. Math. 250 (1971), 107-108. | MR | Zbl

[6] H. Hasse, Number Theory. Springer, 1980. | MR | Zbl

[7] P. Kaplan, K.S. Williams, Representation of Primes in Arithmetic Progressions by Binary Quadratic Forms. J. Number Theory 45 (1993), 61-67. | MR | Zbl

[8] T. Kusaba, Remarque sur la distribution des nombres premiers. C. R. Acad. Sci. Paris Sér. A 265 (1967), 405-407. | MR | Zbl

[9] A. Meyer, Über einen Satz von Dirichlet. J. Reine Angew. Math. 103 (1888), 98-117. | JFM

Cited by Sources: