Monatshefte für Mathematik最新文献

We obtain asymptotic formulae for the second discrete moments of the Riemann zeta function over arithmetic progressions (frac{1}{2} + i(a n + b)). It reveals noticeable relation between the discrete moments and the continuous moment of the Riemann zeta function. Especially, when a is a positive integer, main terms of the formula are equal to those for the continuous mean value. The proof requires the rational approximation of (e^{pi k/a}) for positive integers k.

Starting from the governing equations for a viscous, incompressible fluid, written in a rotating, spherical coordinate system that is valid at the North Pole, the thin-shell approximation is invoked. No further approximations are needed in the derivation of the system of asymptotic equations used here. Suitable stress conditions on the upper and lower surfaces of the ice are described, leading to the construction of a solution for the Transpolar Drift current. This involves the specification of a suitable geostrophic flow, combined with an Ekman component. Then, via the stress conditions across the ice at the surface, a solution for the motion of the ice, and for the associated wind blowing over it, are obtained. In addition, the model adopted here provides a prediction for the reduction in ice thickness along the Transpolar Drift current as it passes through the Fram Strait. The formulation that we present allows considerable freedom in the choices of the various elements of the flow; the model chosen for the physical properties of the ice is particularly significant. All these aspects are discussed critically, and it is shown that many avenues for future investigation have been opened.

In this note, we prove the last remaining case of the original 15 two-term supercongruence conjectures for sporadic sequences. The proof utilizes a new representation for this sequence (due to Gorodetsky) as the constant term of powers of a Laurent polynomial.

Let (f in S_{k}(Gamma _{0}(N))) be a normalized Hecke eigenforms of integral weight k and level (N ge 1). In the article, we establish the asymptotics of power moment associated to the sequences ({lambda _{f otimes f otimes f}(mathcal {Q}(underline{x}))}_{mathcal {Q} in mathcal {S}_{D}, underline{x} in mathbb {Z}^{2}}) and ({lambda _{f otimes mathrm{sym^{2}}f}(mathcal {Q}(underline{x}))}_{mathcal {Q} in mathcal {S}_{D}, underline{x} in mathbb {Z}^{2}}) where (mathcal {S}_{D}) denotes the set of inequivalent primitive integral positive-definite binary quadratic forms (reduced forms) of fixed discriminant (D < 0.) As a consequence, we prove results concerning the behaviour of sign changes associated to these sequences.

This article is about the periodic points characterization of automorphisms of some solenoids, whose duals are subgroups of algebraic number fields. Here, we use the theory of adeles for describing a solenoid and the periodic points of its automorphisms. This is in line with the earlier characterizations which considered other classes of solenoids.

In this article, we investigate large prime factors of Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms in short intervals. One of the new ingredients involves deriving an explicit version of Chebotarev density theorem in an interval of length (frac{x}{(log x)^A}) for any (A>0), modifying an earlier work of Balog and Ono. Furthermore, we need to strengthen a work of Rouse-Thorner to derive a lower bound for the largest prime factor of Fourier coefficients in an interval of length (x^{1/2 + epsilon }) for any (epsilon >0).

N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in terms of so-called associated weight functions. These functions are frequently appearing in the theory of ultradifferentiable function classes and in this setting additional information is available since associated weight functions are defined in terms of a given weight sequence. We express and characterize several known properties for N-functions purely in terms of weight sequences which allows to construct (counter-) examples. Moreover, we study how for abstractly given N-functions this framework becomes meaningful and finally we establish a connection between the complementary N-function and the recently introduced notion of the so-called dual sequence.

Let G be a Beauville p-group. If G exhibits a ‘good behaviour’ with respect to taking powers, then every lift of a Beauville structure of (G/Phi (G)) is a Beauville structure of G. We say that G is a Beauville p-group of wild type if this lifting property fails to hold. Our goal in this paper is twofold: firstly, we fully determine the Beauville groups within two large families of p-groups of maximal class, namely metabelian groups and groups with a maximal subgroup of class at most 2; secondly, as a consequence of the previous result, we obtain infinitely many Beauville p-groups of wild type.