On the hybrid mean value of Cochrane sums and generalized Kloosterman sums
On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
On the ideal class groups of the maximal real subfields of number fields with all roots of unity
In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
On the identities of symmetry for the generalized Bernoulli polynomials attached to of higher order.
On the identities of symmetry for the -Euler polynomials of higher order.
On the image of -adic Galois representations for abelian varieties of type I and II.
On the image of -adic Galois representations
We explore the question of how big the image of a Galois representation attached to a -adic modular form with no complex multiplication is and show that for a “generic” set of -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.
On the imbeddings of imaginary quadratic orders in definite quaternion orders.
On the incongruence of consecutive fourth powers.
On the independence of σ(ϕ(n)) and ϕ(σ(n))
On the index of an odd perfect number
Suppose that N is an odd perfect number and is a prime power with . Define the index . We prove that m cannot take the form , where u is a positive integer and 2u+1 is composite. We also prove that, if q is the Euler prime, then m cannot take any of the 30 forms q₁, q₁², q₁³, q₁⁴, q₁⁵, q₁⁶, q₁⁷, q₁⁸, q₁q₂, q₁²q₂, q₁³q₂, q₁⁴ q₂, q₁⁵q₂, q₁²q₂², q₁³q₂², q₁⁴q₂², q₁q₂q₃, q₁²q₂q₃, q₁³q₂q₃, q₁⁴q₂q₃, q₁²q₂²q₃, q₁²q₂²q₃², q₁q₂q₃q₄, q₁²q₂q₃q₄, q₁³q₂q₃q₄, q₁²q₂²q₃q₄, q₁q₂q₃q₄q₅, q₁²q₂q₃q₄q₅, q₁q₂q₃q₄q₅q₆,...
On the index of length four minimal zero-sum sequences
Let G be a finite cyclic group. Every sequence S over G can be written in the form where g ∈ G and , and the index ind(S) is defined to be the minimum of over all possible g ∈ G such that ⟨g⟩ = G. A conjecture says that every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. This conjecture was confirmed recently for the case when |G| is a product of at most two prime powers. However, the general case is still open. In this paper, we make some...
On the index of sequences over cyclic groups
On the index of the boundary points of four-dimensional lattices that are admissible for a cube.
On the indices of multiquadratic number fields
On the infinite fern of Galois representations of unitary type
Let be a CM number field, an odd prime totally split in , and let be the -adic analytic space parameterizing the isomorphism classes of -dimensional semisimple -adic representations of satisfying a selfduality condition “of type ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in has dimension at least . As important steps, and in any rank, we prove that any first order...
On the infinite product exponents of meromorphic modular forms for certain arithmetic groups
On the infinite volume Hecke surfaces
On the inhomogeneous Hall's ray of period-one quadratics.
On the Injectivity of the Map of the Witt Group of a Scheme into the Witt Group of its Function Field.