A note on zeta-functions of algebraic number fields
A note on |αp - q|
A note to a bifurcation result of H. Kielhöfer for the wave equation
A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.
A note to the rationality of infinite series. I
A note to the transcendence of special infinite series
A notion of density and essential components in GF[p,x]
A notion of diaphony based on p-adic arithmetic
A number-theoretic conjecture and its implication for set theory.
A numerical bound for small prime solutions of some ternary linear equations
A numerical sampling problem and the Weyl pseudorandom numbers.
A -adic measure attached to the zeta functions associated with two elliptic modular forms. II
Let and be holomorphic common eigenforms of all Hecke operators for the congruence subgroup of with “Nebentypus” character and and of weight and , respectively. Define the Rankin product of and bySupposing and to be ordinary at a prime , we shall construct a -adically analytic -function of three variables which interpolate the values for integers with by regarding all the ingredients , and as variables. Here is the Petersson self-inner product of .
A -adic regulator map and finiteness results for arithmetic schemes.
A -adic study of the partial sums of the harmonic series.
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 Nevanlinna-Diophantine correspondence
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 paintability version of the combinatorial Nullstellensatz, and list colorings of -partite -uniform hypergraphs.
A parametric family of elliptic curves
A parametric family of quartic Thue equations