Geodesic
Class Numbers and Biquadratic Reciprocity
Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 969-988

Voir la notice de l'article provenant de la source Cambridge University Press

0. Notation. Throughout this paper p denotes a prime congruent to 1 modulo 4. It is well known that such primes are expressible in an essentially unique manner as the sum of the squares of two integers, that is, (0.1) with |a| and |b| uniquely determined by (0.1). Since a is odd, replacing a by –a if necessary, we can specify a uniquely by (0.2) Further, as {[(p – l)/2]!}2 = – 1 (mod p), we can specify b uniquely by (0.3) These choices are assumed throughout.The following notation is also used throughout the paper: h(d) denotes the class number of the quadratic field of discriminant d, (d/n) is the Kronecker symbol of modulus |d|, [x] denotes the greatest integer less than or equal to the real number x, and {x} = x – [x]. 
Williams, Kenneth S.; Currie, James D. Class Numbers and Biquadratic Reciprocity. Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 969-988. doi: 10.4153/CJM-1982-070-x
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