Gun, Sanoli ; Ramakrishnan, B. (2008) On special values of certain Dirichlet L-functions The Ramanujan Journal, 15 (2). pp. 275-280. ISSN 1382-4090
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Official URL: http://doi.org/10.1007/s11139-007-9077-x
Related URL: http://dx.doi.org/10.1007/s11139-007-9077-x
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer Nature. |
| Keywords: | Dirichlet L-Functions; Sums Of Squares. |
| ID Code: | 118027 |
| Deposited On: | 11 May 2021 07:16 |
| Last Modified: | 11 May 2021 07:16 |
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