Volume 4, Issue 2-1, March 2015, Page: 1-6
Class Number Formula for Certain Imaginary Quadratic Fields
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
Received: Oct. 26, 2014;       Accepted: Nov. 6, 2014;       Published: Nov. 29, 2014
DOI: 10.11648/j.pamj.s.2015040201.11      View  3115      Downloads  159
Abstract
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).
Keywords
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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