Abstract
In the first part of the paper, we discuss two different definitions of the Hilbert symbol and prove their equivalence. The second part is devoted to a detailed consideration of the one-dimensional case for an arbitrary prime number p (odd as well as even). At the end of the article, we give explicit formulas in the general case of a multidimensional local field for both cases of different and mixed characteristics, for an arbitrary prime number. Bibliography: 25 titles.
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Belyaeva, T.B., Vostokov, S.V. The Hilbert Symbol in a Complete Multidimensional Field. I. Journal of Mathematical Sciences 120, 1483–1500 (2004). https://doi.org/10.1023/B:JOTH.0000017880.47115.ae
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DOI: https://doi.org/10.1023/B:JOTH.0000017880.47115.ae