ABSTRACT
Let p be a prime number. ℤp and ℚ p https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072614/3ce7aa8c-759e-436c-a799-e22f41c5a790/content/eq1086.tif"/> denote, respectively, the ring of p-adic integers and the field of p-adic numbers, K is a non-archimedean non trivially valued complete field with valuation | ⋅ | https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072614/3ce7aa8c-759e-436c-a799-e22f41c5a790/content/eq1087.tif"/> . We suppose that ℚ p ⊂ K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072614/3ce7aa8c-759e-436c-a799-e22f41c5a790/content/eq1088.tif"/> . The space of all continuous functions f : ℤ p → K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072614/3ce7aa8c-759e-436c-a799-e22f41c5a790/content/eq1089.tif"/> , equipped with the supremum norm ‖ ⋅ ‖ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072614/3ce7aa8c-759e-436c-a799-e22f41c5a790/content/eq1090.tif"/> , will be denoted by C(ℤp → K). The degree of a polynomial p will be denoted deg p.
