Tate duality and ramification of division algebras
Tate duality and wild ramification.
The absolute Galois group of a pseudo p-adically closed field.
The adelic zeta function associated to the space of binary cubic forms. II: Local theory.
The Affine Frame in -adic Analysis
In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of -adic number, hence provide new mathematic tools for application of -adic analysis.
The asymptotic behaviour of the number of solutions of polynomial congruences.
The average distribution of cubic exponential sums.
The Behavior of Rigid Analytic Functions Around Orbits of Elements of <>
The construction of unramified abelian cubic extensions of a quadratic field
The Deuring-Safarevic Formula Revisited.
The dilogarithm and the norm residue symbol
The expected number of zeros of a random system of -adic polynomials.
The Fekete-Szegő theorem with splitting conditions: Part I
The field-of-norms functor and the Hilbert symbol for higher local fields
The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.
The formulas for the coefficients of the sum and product of p-adic integers with applications to Witt vectors
The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of -functions...
The Galois group of
The group of -adic integers.
The Hasse norm principle in non-abelian extensions.
The Heisenberg uncertainty relation in harmonic analysis on -adic numbers field
In this paper, two important geometric concepts–grapical center and width, are introduced in -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on -adic numbers field.