Class Number Formula for Certain Imaginary Quadratic Fields
Pure and Applied Mathematics Journal
Volume 4, Issue 2-1, March 2015, Pages: 1-6
Received: Oct. 26, 2014; Accepted: Nov. 6, 2014; Published: Nov. 29, 2014
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N. L. Wang, Dept. of Appl. Math., Shangluo Univ. Shangluo,726000, PRC
T. Arai, Dept. of Appl. Math., Shangluo Univ. Shangluo,726000, PRC; Grad. School of Advances Tech. Kinki Univ., Iizuka, 820-8555, Japan
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In this note we shall show how Carlitz in 1954 could have reached an analogue of the Voronoi congruence in the more difficult case of p≡1(mod4): h(-4p) ≡B(p+1)/2(x4)(mod p), where B(p+1)/2(x4) is the generalized Bernoulli number with x4 being the Kronecker symbol associated to the Gaussian field Q(√-4).
Class Number Formula, Short Interval Character Sum, Generalized Bernoulli Number, Euler Number
To cite this article
N. L. Wang, T. Arai, Class Number Formula for Certain Imaginary Quadratic Fields, Pure and Applied Mathematics Journal. Special Issue: Abridging over Troubled Water---Scientific Foundation of Engineering Subjects. Vol. 4, No. 2-1, 2015, pp. 1-6. doi: 10.11648/j.pamj.s.2015040201.11
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