Some Invariants of Zd-p-Extensions.
Some linear relations between values of trigonometric functions at kπ/n
Some meromorphic functions associated to the S-unit equation
Some methods for evaluating the regulator of a real quadratic function field.
Some more long continued fractions, I
Some new maps and ideals in classical Iwasawa theory with applications
We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. This leads to a new and unifying framework for the Iwasawa theory of such fields including a real analogue of Stickelberger’s Theorem,...
Some non-semi-simple Iwasawa modules
Some p-adic Galois Representations for Curves in Characteristic p.
Some problems concerning roots of polynomials with Dirichlet characters as coefficients
Some problems in multidimensional analytic number theory
Some properties of orders of quaternion algebras with regard to the discrete norm
Quaternion algebras are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Some quartic number fields containing an imaginary quadratic subfield
Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.
Some Recent Developments in three Classical Problems of Number Theory.
Some remarks about the power residue symbol
Some remarks on conjectures about cyclotomic fields and -groups of
Some remarks on factorization in algebraic number fields
Some remarks on Hilbert-Speiser and Leopoldt fields of given type
Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers in L is free as a module over the associated order . We also give examples, some of which show that this result can still hold without the assumption that K contains...
Some Remarks on Leopoldt's Conjecture.
Some remarks on L-functions and class numbers
Some remarks on the decomposition of a rational prime in a Galois extension