Showing papers in "Journal of Number Theory in 1984"

TL;DR: In this article, the same authors proved that ∣S∣ ≥ ∣A∣ + 1 2 ∣B∣ unless C + (−B + B) = C.

TL;DR: In this paper, the vector space of cuspidal cohomology of certain congruence subgroups of SL(3, Z ) was found and the action of the Hecke operators on this space was determined.

TL;DR: In this paper, it was shown that the Dirichlet series T(s, z) is a meromorphic function of the Riemann zeta function and its poles and residues are determined.

TL;DR: The view-obstruction problem for C is the problem of finding the constant K(C) defined to be the lower bound of those α such that any half-line L given by xi = ait (i = 1, 2, …, n), where the ai (1 ≤ i ≤ n) are positive real numbers and the parameter t runs through [0, ∞, intersects Δ(C, α) as mentioned in this paper.

TL;DR: The existence of explicit numerical zero-free regions for Dirichlet L-functions with characters modulo k has been shown in this article, where it is shown that the only possible zero in this region is a simple real zero arising from an L-function formed with a real non-principal character.

TL;DR: In this paper, a simple proof for a reciprocity formula for sums of cotangent functions is presented, where the second arguments are zero and the sums are four times the original Dedekind sums.

TL;DR: For a given sequence ω = (x(k))k=0∞ in Us, U = R/Z, let S(ω) denote the set of all boxes I in Us with bounded discrepancy function, i.e., lI the characteristic function of I.

TL;DR: In this paper, it was shown that R K > c d ( log γ d D K ) r(K)−ρ(K ) for constants c d, γ D > 0 depending only on d.

TL;DR: In this paper, it was shown that if G is a split extension of a cyclic p-group with faithful action, then any torsion unit of augmentation one of Z G is rationally conjugate to a group element.

TL;DR: In this paper, it was shown that for any generalization of relative natural density (obeying a few basic assumptions) if a value is assigned to the relative density of primes of lead digit 1 then this value is always log 10 2.

TL;DR: The three numbers 1, 5, 10 have the property that the product of any two numbers decreased by 1 is a perfect square as mentioned in this paper, and it is proved that there is no other positive integer N which shares this property with 1,5, and 10.

TL;DR: Elliott's generalization of the Turan-Kubilius inequality is further generalized by establishing an upper bound for the sum Σ n ≤ x F (∣ f ( n ) − A ∣), where f is a complex-valued additive arithmetical function, A an arbitrary number and F an arbitrary nonnegative-valued increasing function.

TL;DR: In this article, the Voronoi-Atkinson formula for Dirichlet polynomials is proved for the case when all the a(n) coefficients of a cusp form are real.

TL;DR: In this article, the concept of an m-regular prime, p, is introduced and it is shown that for certain values of m, the Fermat equation with exponent p has no nontrivial solutions over the field Q(√m).

TL;DR: Asymptotic formulas on the average values of the "sum of digits" function and the average numbers of occurrences of fixed subblocks in Cantor representations of integers are established in this article.

TL;DR: In this paper, a lower bound for the p-adic rank of the group of units in the general case of a Galois number field over the rationals is given, and the same method is also applied to the case of p -units.

TL;DR: In this paper, Nettler proved the algebraic independence of A and B under almost the same condition and furthermore a result concerning the transcendence of AB is established, where the a's and b's are positive integers satisfying a certain mutual growth condition.

TL;DR: In this paper, the continued fraction convergents to a random real number were shown to approximate that number with a limiting probability distribution that had been conjectured by H. W. Lenstra.

TL;DR: In this article, a ladder of dilogarithms of powers of an algebraic base is constructed and shown to have significant properties when the powers are divisors of the highest power in the relation.

TL;DR: In this paper, it was shown that the space of global solutions of a Skolem problem is dense in the spaces of adelic solutions, which implies that there exists a decision procedure for Skoleme problems, because the corresponding local problems are decidable.

TL;DR: In this paper, the least positive residue of an integer x modulo m is defined, and if x, m is odd then |R(ab′)|a,b∈A = −21−n(∏χ(Σa = 1m − 1 aχ (a))).

TL;DR: In this article, the number of variables required to solve p-adic systems of homogeneous and inhomogeneous additive equations, as well as single homogeneous equations in general, is studied.

TL;DR: In this article, the relation between the 4-ranks of various quadratic number fields is investigated using the classical criterion of Redei and Reichardt, and the classical 4-rank criterion is applied.

TL;DR: In this article, it was proved that every integer exceeding exp(exp(13.97)) is a sum of seven positive integral cubes, and some conjectures concerning the representation of integers as sum of nonnegative integral cubes are also discussed.

TL;DR: In this paper, a close relation between K and the genus group of k is established, and it is shown that Kk has a relative integral basis (RIB) (i.e., OK is free over Ok) iff N(e0) = −1 and w = 1, where e0 is the fundamental unit of k.

TL;DR: In this paper, it was shown that there are 21 positive integers n such that n ∈ S and n ≡ 1, 2, 5, 6 (mod 8) with odd discriminant and class number 1 or 2.

TL;DR: In this article, the asymptotic behavior of the Dickman function p(u) with respect to a delay differential equation has been studied, where pa(u), where p is prime and p is p|n, has been shown to be a function whose behavior is similar to that of the one of the delay-deterministic Dickman functions.

TL;DR: In this paper, the diophantine equation of the title has been solved by Ljunggren, by indirect use of the p-adic method (use is made of intermediate algebraic extensions).