The non-abelian normal CM-fields of degree 36 with class number one
The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent
The Non-p-Part of the Class Number in a Cyclotomic ...p-Extension.
The Normal Density of Prime Ideals in Small Regions.
The number of different lengths of irreducible factorization of a natural number in an algebraic number field
The number of irreducible factors of a polynomial, II
The number of real quadratic fields having units of negative norm.
The number of S₄-fields with given discriminant
The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders
Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.
The period-index problem in WC-groups IV: a local transition theorem
Let be a complete discretely valued field with perfect residue field . Assuming upper bounds on the relation between period and index for WC-groups over , we deduce corresponding upper bounds on the relation between period and index for WC-groups over . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and...
The Piltz divisor problem in number fields: An improved lower bound by Soundararajan's method
The Pólya-Vinogradov inequality for totally real algebraic number fields
The polylogarithm in the field of two irreducible quintics.
The Prime Ideal Theorem in Non-Commutative Arithmetic.
The product of linear forms in a field of series and the Riemann hypothesis for curves
The Quadratic Schur Subgroup over Local and Global Fields.
The R₂ measure for totally positive algebraic integers
Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates are positive real numbers. We study the set ₂ of the quantities . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.
The Rational Invariants of the Tame Quivers.
The reduced ideals of a special order in a pure cubic number field
Let be a pure cubic field, with , where is a cube-free integer. We will determine the reduced ideals of the order of which coincides with the maximal order of in the case where is square-free and .
The refined p-adic abelian Stark conjecture in function fields.