Rational quartic reciprocity

Franz Lemmermeyer

Acta Arithmetica (1994)

  • Volume: 67, Issue: 4, page 387-390
  • ISSN: 0065-1036

How to cite

top

Franz Lemmermeyer. "Rational quartic reciprocity." Acta Arithmetica 67.4 (1994): 387-390. <http://eudml.org/doc/206639>.

@article{FranzLemmermeyer1994,
author = {Franz Lemmermeyer},
journal = {Acta Arithmetica},
keywords = {quartic field; Jacobi symbols; rational reciprocity laws},
language = {eng},
number = {4},
pages = {387-390},
title = {Rational quartic reciprocity},
url = {http://eudml.org/doc/206639},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Franz Lemmermeyer
TI - Rational quartic reciprocity
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 4
SP - 387
EP - 390
LA - eng
KW - quartic field; Jacobi symbols; rational reciprocity laws
UR - http://eudml.org/doc/206639
ER -

References

top
  1. [1] K. Burde, Ein rationales biquadratisches Reziprozitätsgesetz, J. Reine Angew. Math. 235 (1969), 175-184. Zbl0169.36902
  2. [2] G. Lejeune Dirichlet, Recherche sur les diviseurs premiers d'une classe de formules du quatrième degré, J. Reine Angew. Math. 3 (1828), 35-69; Werke I , 63-98. 
  3. [3] R. Evans, Residuacity of primes, Rocky Mountain J. Math. 19 (1989), 1069-1081. Zbl0699.10012
  4. [4] A. Fröhlich, The restricted biquadratic residue symbol, Proc. London Math. Soc. (3) 9 (1959), 189-207. Zbl0087.03301
  5. [5] T. Gosset, On the law of quartic reciprocity, Mess. Math. (2) 41 (1911), 65-90. Zbl42.0212.03
  6. [6] E. Lehmer, Criteria for cubic and quartic residuacity, Mathematika 5 (1958), 20-29. Zbl0102.28002
  7. [7] E. Lehmer, Rational reciprocity laws, Amer. Math. Monthly 85 (1978), 467-472. Zbl0383.10003
  8. [8] L. Rédei, Über die Grundeinheit und die durch 8 teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper, J. Reine Angew. Math. 171 (1934), 131-148. Zbl0009.29302
  9. [9] A. Scholz, Über die Lösbarkeit der Gleichung t²-Du²=-4, Math. Z. 39 (1934), 95-111. Zbl0009.29402
  10. [10] B. A. Venkov, Elementary Number Theory, Moscow, 1937 (in Russian); English transl.: H. Alderson (ed.), Wolters-Noordhoff, Groningen, 1970. 
  11. [11] K. S. Williams, K. Hardy and C. Friesen, On the evaluation of the Legendre symbol ((A+B√m)/p), Acta Arith. 45 (1985), 255-272. Zbl0524.10002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.