On special values of certain Dirichlet L-functions |
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Authors: | Sanoli Gun B. Ramakrishnan |
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Affiliation: | (1) Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211 019, India |
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Abstract: | Let r k (n) denote the number of ways n can be expressed as a sum of k squares. Recently, S. Cooper (Ramanujan J. 6:469–490, [2002]), conjectured a formula for r 9(t), t≡5 (mod 8), r 11(t), t≡7 (mod 8), where t is a square-free positive integer. In this note we observe that these conjectures follow from the works of Lomadze (Akad. Nauk Gruz. Tr. Tbil. Mat. Inst. Razmadze 17:281–314, [1949]; Acta Arith. 68(3):245–253, [1994]). Further we express r 9(t), r 11(t) in terms of certain special values of Dirichlet L-functions. Combining these two results we get expressions for these special values of Dirichlet L-functions involving Jacobi symbols. |
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Keywords: | Dirichlet L-functions Sums of squares |
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