A new approach to -Bernoulli numbers and -Bernoulli polynomials related to -Bernstein polynomials.
A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
A new -analogue of Bernoulli polynomials associated with -adic -integrals.
A note on Euler number and polynomials.
A note on functional equations of the -adic polylogarithms
A note on Nörlund-type twisted -Euler polynomials and numbers of higher order associated with fermionic invariant -integrals.
A note on normal and power bases
A note on power series representations in local fields
A note on some expansions of p-adic functions
Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by . The system is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to . This paper is a remark to Rutkowski’s paper. We define another system in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...
A note on the multiple twisted Carlitz's type -Bernoulli polynomials.
A note on the -adic Galois representations attached to Hilbert modular forms.
A note on the -adic gamma function
A note on the -Euler measures.
A note on the -Genocchi numbers and polynomials.
A note on trilinear forms for reducible representations and Beilinson's conjectures
We extend Prasad’s results on the existence of trilinear forms on representations of of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.
A note on Waring's problem in p-adic fields
A p-adic integral representation of the p-adic L-function.
A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I.
A p-adic Perron-Frobenius theorem
We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.
A Rankin-Selberg integral for the adjoint representation of GL3.