20190501, 10:12  #1 
Mar 2016
2·3·71 Posts 
quadratic reciprocity law
A peaceful day for all members,
Does there exist only one quadratic reciprocity law, or do there exist several quadrac reciprocity laws depending on the quadratic polyonoms, resp. is the quadratic reciprocity law the same for gaussian and eisenstein primes. https://en.wikipedia.org/wiki/Reciprocity_law https://en.wikipedia.org/wiki/Gaussi...aussian_primes https://en.wikipedia.org/wiki/Eisenstein_prime Thanks in advance for a clear answer, Bernhard 
20190501, 11:06  #2 
Sep 2003
3×863 Posts 

20190501, 13:59  #3  
Feb 2017
Nowhere
2^{6}·3^{2}·11 Posts 
Quote:
It should be possible to formulate quadratic reciprocity for the Eisenstein integers. I'm not sure how, offhand. 

20190501, 14:33  #4 
Dec 2012
The Netherlands
2·3·5·61 Posts 
See chapter 9 "Cubic and Biquadratic Reciprocity" in the famous book
"A Classical Introduction to Modern Number Theory" (2nd edition) by Ireland & Rosen (published by Springer). https://www.springer.com/us/book/9780387973296 
20190501, 15:53  #5  
Sep 2003
3·863 Posts 
Quote:


20190502, 16:14  #6 
Feb 2017
Nowhere
2^{6}·3^{2}·11 Posts 

20190603, 23:26  #7 
Mar 2016
426_{10} Posts 
A peaceful night for you,
is there a special quadratic reciprocity law for the polynomial f(n)=2n^21 ? It might be also interesting for other persons. Greetings from the "even primes" Bernhard 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
7th power reciprocity  carpetpool  Miscellaneous Math  3  20181014 13:32 
Lucas number cubic and quadratic reciprocity  carpetpool  Miscellaneous Math  0  20180627 03:12 
Basic Number Theory 17: quadratic reciprocity  Nick  Number Theory Discussion Group  0  20170131 14:41 
Quadratic Residues  Romulas  Math  3  20100509 03:27 
mistype in Law of quadratic reciprocity page?  LLL  mersennewiki  1  20081216 15:34 