Discrete universality of the <Emphasis Type="Italic">L</Emphasis>-functions of elliptic curves

A discrete universality theorem is obtained in the Voronin sense for the L-functions of elliptic curves. We use the difference of an arithmetical progression h > 0 such that \(\exp \left\{ {\frac{{2\pi k}}{h}} \right\}\) is rational for some k ≠ 0. A limit theorem in the space of analytic functions plays a crucial role in the proof.     

The value distribution of Artin L-series and zeros of Zeta-functions

We prove a so-called (joint) universality property of Artin L-functions. Our work is a generalization of a theorem of Voronin on Dirichlet L-functions (The Riemann Zeta-function, Walter de Gruyter, Berlin, 1992). So far we extend the theory of Harald Bohr, Jessen, Titchmarsh and Voronin on the value distributions of the Riemann Zeta-function and Dirichlet L-series. Our proofs are independent of Artin's conjecture on the holomorphy of Artin L-functions with non-trivial characters.In the applications, we prove that Zeta-functions of ideal classes of an arbitrary number field have infinitely many zeros in the strip , provided that the class group is non-trivial. Further applications concern the functional independence of Dedekind Zeta-functions of normal extensions and of Artin L-functions.     

On the joint universality of periodic zeta functions

In this paper, we obtain the joint universality (in the sense of Voronin) of Dirichlet series with periodic multiplicative coefficients. The proof is based on a joint limit theorem in the space of analytic functions.     

On a Generalization of Voronin’s Theorem

Mathematical Notes - Voronin’s theorem states that the Riemann zeta-function ζ(s) is universal in the sense that all analytic functions that are defined and have no zeros on the right...     

Linear twists of L-functions of degree 2 from the Selberg class

In 1983, S. M. Voronin obtain an analytic continuation to the entire complex plane for some twists of L-functions associated with holomorphic modular forms on SL(2, Z). In this paper, we extend Voronin’s result to L-functions of degree 2 from the extended Selberg class.     

On universality for linear combinations of L-functions

In the present paper, we consider the universality property in the Voronin sense for certain combinations of L-functions with general Dirichlet series as coefficients. In addition, we present some interesting examples of zeta and L-functions which can be expressed in this form. More precisely, we obtain the universality theorem for zeta functions associated to certain arithmetic functions, zeta functions associated to symmetric matrices and Euler–Zagier double zeta and L-functions.     

Universality of the Riemann zeta-function

In 1975, S.M. Voronin proved the universality of the Riemann zeta-function ζ(s). This means that every non-vanishing analytic function can be approximated uniformly on compact subsets of the critical strip by shifts ζ(s+iτ). In the paper, we consider the functions F(ζ(s)) which are universal in the Voronin sense.     

Bartle-Graves Theorem Revisited

We take a fresh look at the Bartle-Graves theorem pointing out the main differences with the standard implicit function theorem. We then present a set-valued version of this theorem which generalizes some recent results. Applications to variational inequalities and differential inclusions are also given.

     

A Riemann-type theorem for a Riemann-type integral

For functions which are Henstock–Kurzweil integrable but not Lebesgue-integrable we prove a theorem which resembles the Riemann theorem on the rearrangement of conditionally convergent series.

     

Beiträge zur Shannonschen Informationstheorie im Falle nichtstationärer Kanäle

Coding theorem and strong converse of the coding theorem are proved for nonstationary semicontinous channels and for almost periodic channels with unknown phase. More general cases are considered.

---

---

Die Arbeit entstand teilweise im Rahmen eines von der Deutschen Forschungsgemeinschaft finanzierten Forschungsvorhabens.

---

Herrn ProfessorJacobs gilt mein besonderer Dank für zahlreiche Anregungen.     

Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.

     

Un teorema di esistenza per controlli ottimi di sistemi definiti da equazioni integrali di Urysohn

Summary In this paper an existence theorem is proved for optimal control problems described by Urysohn systems, with pointwise constraints on controls and states. An example of application of the existence theorem is given.

---

---

Entrata in Redazione il 15 marzo 1978.

---

Lavoro eseguito nell'ambito della mia attività di ricerca come borsista C.N.R., presso l'Università di Genova.     

Letter to the Editor: A Short Complex-Variable Proof of the Titchmarsh Convolution Theorem

The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theorem for bounded holomorphic functions on the unit disk.

     

Ein einfacher Beweis des Satzes von Alexandroff-Lester

By presenting counterexamples and a new proof, we determine all metric vector spaces, for which the theorem of ALEXANDROFF-LESTER holds. In this context, the theorem will be extended to certain nonregular metric vector spaces of characteristic 2.

---

---

Dedicated to Professor Giuseppe Tallini on the occasion of his 60th birthday

---

Herrn H. Lenz danke ich für mehrere Vorschläge zur durchsichtigeren Formulierung der Beweise.     

Eine Bemerkung über den speziellen Bezoutschen Satz

Some synthetic methods in a projective space are devellopped and using them a theorem connected with the theorem of Bézout is proved without using any postulation about algebraic closure.

---

---

Herrn Professor Dr. WERNER BURAU zum 70. Geburtstag     

Ein funktionalanalytischer Beweis des Satzes von Cauchy-Kowalewsky

Using functional analytic methods, in particular the fixed point theorem of Schauder-Tychonoff, a new and short proof is given for the classical Cauchy-Kowalewsky theorem on analytic partial differential equations.

---

---

Herrn Prof. Dr. F.W. Schafke zum 60. Geburtstag gewidmet     

A new version of a theorem of Kaplansky

Abstract

A well-known theorem of Kaplansky states that any projective module is a direct sum of countably generated modules. In this paper, we prove the w-version of this theorem, where w is a hereditary torsion theory for modules over a commutative ring.

Communicated by Silvana Bazzoni     

A Girsanov Type Theorem on the Path Space Over a Compact Riemannian Manifold

Abstract

This article establishes a Girsanov type theorem on path spaces over compact Riemannian manifolds, generalizing the classical Girsanov theorem for Euclidean spaces.     

Morley’s trisector Theorem for isosceles tetrahedron

We extend Morley’s trisector theorem in the plane to an isosceles tetrahedron in three-dimensional space. We will show that the Morley tetrahedron of an isosceles tetrahedron is also isosceles tetrahedron. Furthermore, by the formula for distance in barycentric coordinate, we introduce and prove a general theorem on an isosceles tetrahedron.

     

A Characterization of the Standard Tori in C2 as Compact Lagrangian ξ-Submanifolds*

In this paper, the authors give a characterization theorem for the standard tori S¹(a) × S¹(b), a, b > 0, as the compact Lagrangian ξ-submanifolds in the two-dimensional complex Euclidean space C² , and obtain the best version of a former rigidity theorem for compact Lagrangian ξ-submanifold in C² . Furthermore, their argument in this paper also proves a new rigidity theorem which is a direct generalization of a rigidity theorem by Li and Wang for Lagrangian self-shrinkers in C².