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• W2103670885 abstract "Abstract For every integer k ≧ 2 we introduce an analytic function of a positive real variable and give a universal formula expressing the values ζ (ℬ, k ) of the zeta functions of narrow ideal classes in real quadratic fields in terms of this function and its derivatives up to order k − 1 evaluated at reduced real quadratic irrationalities associated to ℬ. We show that our functions satisfy functional equations and use these to deduce explicit formulas for the rational numbers ζ (ℬ, 1 − k ). We also give an interpretation of our formula for ζ (ℬ, k ) in terms of cohomology groups of SL(2, ℤ) with analytic coefficients and describe a “twisted” extension of the main formula that allows one to treat zeta values of zeta functions of ray classes rather than just ideal classes. Finally, we use our formulas to compute some zeta-values numerically and test that they are expressible as combinations of higher polylogarithm functions evaluated at algebraic arguments." @default.
• W2103670885 created "2016-06-24" @default.
• W2103670885 creator A5005589416 @default.
• W2103670885 creator A5031688833 @default.
• W2103670885 date "2013-06-01" @default.
• W2103670885 modified "2023-10-11" @default.
• W2103670885 title "Higher Kronecker “limit” formulas for real quadratic fields" @default.
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• W2103670885 doi "https://doi.org/10.1515/crelle.2012.022" @default.
• W2103670885 hasPublicationYear "2013" @default.
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