Evaluation of the infinite series $\sum ^ \infty _ {n=1,(\frac np)=1}(\frac np)_ 4{}n^ {-1}$
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- by Kenneth Hardy and Kenneth S. Williams PDF
- Proc. Amer. Math. Soc. 109 (1990), 597-603 Request permission
Abstract:
Let $p$ be a prime $\equiv 1(\bmod 4)$. The value of the infinite series $\sum \nolimits _{_{(\tfrac {n}{p}) = 1}^{n = 1}}^\infty {{{(\tfrac {n}{p})}_4}{n^{ - 1}}}$ is given in finite terms.References
- Robert L. Long, Algebraic number theory, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 41, Marcel Dekker, Inc., New York-Basel, 1977. MR 0469888
- J. H. Loxton, Some conjectures concerning Gauss sums, J. Reine Angew. Math. 297 (1978), 153β158. MR 460250, DOI 10.1515/crll.1978.297.153 C. R. Mathews, Gauss sums and elliptic functions. II. The quartic sum, Institut des Hautes Γtudes Scientifiques, Bures-sur-Yvette, France, April 1979 (IHES/M/79/267).
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 597-603
- MSC: Primary 11M20; Secondary 11L05, 11N13
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019275-7
- MathSciNet review: 1019275