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In this article, using the arithmetic of Hurwitz zeta functions and Gauss sums, we investigate the arithmetic nature of ζ K (2 k + 1) ζ K + (2 k + 1) , where K is any totally imaginary abelian extension with maximal totally real subfield K + and k ≥ 1 is an integer. As a consequence, we derive an elementary proof of the elegant result of Murty and Pathak about irrationality of Dedekind zeta values associated to imaginary quadratic fields at odd integers. This alternate line of action allows us to link these questions to a question of Chowla and Milnor, resulting in some new results about Dedekind zeta values. [ABSTRACT FROM AUTHOR]

We study the class number one and class number two problems for real quadratic fields Q (9 m 2 + 4 m) , where m is an odd integer. We show that for m ≡ 1 (mod 3) there is only one such field with class number one and only one such field with class number two. Moreover, we also evaluate some generalized Dedekind sums. [ABSTRACT FROM AUTHOR]