Construction of 2-adic Chebyshev polynomials

Abstract. Several 2-adic cosine and sine functions are constructed on the 2-adic field expressed by the \(\tilde{\mathbb S}\)-valued exponential functions and the characters \(v_n\) of the 2-adic additive group. Then follows the construction of some analogies of the Chebyshev polynomials on the 2-adic field \((\mathbb I,\stackrel{\bullet}{+},\bullet)\) using these cosine and sine functions. Orthogonality of these Chebyshev polynomials is also investigated.