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).
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Pure and Applied Mathematics Journal (Volume 4, Issue 2-1)
This article belongs to the Special Issue Abridging over Troubled Water---Scientific Foundation of Engineering Subjects |
| DOI | 10.11648/j.pamj.s.2015040201.11 |
| Page(s) | 1-6 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Class Number Formula, Short Interval Character Sum, Generalized Bernoulli Number, Euler Number
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APA Style
N. L. Wang, T. Arai. (2014). Class Number Formula for Certain Imaginary Quadratic Fields. Pure and Applied Mathematics Journal, 4(2-1), 1-6. https://doi.org/10.11648/j.pamj.s.2015040201.11
ACS Style
N. L. Wang; T. Arai. Class Number Formula for Certain Imaginary Quadratic Fields. Pure Appl. Math. J. 2014, 4(2-1), 1-6. doi: 10.11648/j.pamj.s.2015040201.11
AMA Style
N. L. Wang, T. Arai. Class Number Formula for Certain Imaginary Quadratic Fields. Pure Appl Math J. 2014;4(2-1):1-6. doi: 10.11648/j.pamj.s.2015040201.11
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Download@article{10.11648/j.pamj.s.2015040201.11,
author = {N. L. Wang and T. Arai},
title = {Class Number Formula for Certain Imaginary Quadratic Fields},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {2-1},
pages = {1-6},
doi = {10.11648/j.pamj.s.2015040201.11},
url = {https://doi.org/10.11648/j.pamj.s.2015040201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040201.11},
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).},
year = {2014}
}
TY - JOUR T1 - Class Number Formula for Certain Imaginary Quadratic Fields AU - N. L. Wang AU - T. Arai Y1 - 2014/11/29 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2015040201.11 DO - 10.11648/j.pamj.s.2015040201.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 6 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040201.11 AB - 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). VL - 4 IS - 2-1 ER -
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