Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 1 (1999), 151-166.
Character sums and the series with applications to real quadratic fields
In this article, let or 1(mod4) be a fundamental discriminant, and let be the real even primitive character modulo . The series can be divided into groups of consecutive terms. Let be any nonnegative integer, an integer, , and let Then . In section 2, Theorems 2.1 and 2.2 reveal asurprising relation between incomplete character sums and partial sums of Dirichlet series. For example, we will prove that for integer if and . In section 3, we will derive algorithm and formula for calculating the class number of a real quadratic field. In section 4, we will attempt to make a connection between two conjectures on real quadratic fields and the sign of .
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 151-166.
First available in Project Euclid: 10 June 2008
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LEU, Ming-Guang. Character sums and the series $L(1,\chi)$ with applications to real quadratic fields. J. Math. Soc. Japan 51 (1999), no. 1, 151--166. doi:10.2969/jmsj/05110151. https://projecteuclid.org/euclid.jmsj/1213108355