Some formulas related to Gauss's sum
Rendiconti del Seminario Matematico della Università di Padova, Tome 41 (1968), pp. 222-226. 
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     author = {Carlitz, L.},
     title = {Some formulas related to {Gauss's} sum},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {222--226},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {41},
     year = {1968},
     mrnumber = {244173},
     zbl = {0186.36202},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_1968__41__222_0/}
}
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Carlitz, L. Some formulas related to Gauss's sum. Rendiconti del Seminario Matematico della Università di Padova, Tome 41 (1968), pp. 222-226. http://archive.numdam.org/item/RSMUP_1968__41__222_0/

[1] S. Chowla, Some formalae of the Gauss sum type (II), Tohokn Mathematical Journal, vol. 32 (1929-30), pp. 352-353. | JFM

[2] S. Ramanujan, Some definite integrals connected with Gauss's sums, Messenger of Mathematics, vol. 44 (1915). pp. 75-85. | JFM