arXiv subjects
Publications and source records attributed to Gene Ward Smith.
The methods of classical invariant theory are used to construct generic polynomials for groups $S_5$ and $A_5$, along with explicit reductions to specializations of the generic polynomials defining any desired field extension with those groups.
Formulas for calculating the Riesz function, introduced by Marcel Riesz in connection with the Riemann hypothesis, are derived; and the behavior of the Riesz function is discussed.
Algebraic methods are used to construct families of unramified abelian extensions of some families of number fields with specified Galois groups.
The analogy between the nth power function and the nth Chebyshev polynomial is pursued, leading to consideration of Chebyshev radicals as analogous to ordinary radicals and Chebyshev exponents to ordinary exponents, and the cosine and hyperbolic cosine as analogs of the exponential function. We then discuss solving polynomial equations in Chebyshev radicals, and apply this to the construction of unramified extensions of quadratic number fields.