Related papers: Explicit Mertens' Theorems for Number Fields

The general solution of M\o ller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.

In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…

In this paper we announce some results obtained for certain algebraic functions, which we call of cyclotomic type. The main results properly resemble von Staudt-Clausen's theorem and Kummer's congruence for the Bernoulli numbers, and such…

We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning Euler systems for the multiplicative group over arbitrary number fields.

A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…

We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations about the local inversion theorem.

A pedagological introduction to effective field theory is presented.

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…

The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold…

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…

We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way,…

In this paper, we prove the universality theorem for the iterated integrals of the logarithm of the Riemann zeta-function on some line parallel to the real axis.

We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…

A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.

A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the general linear…

In the present paper, we provide a new analogy between number fields and 1-dimensional function fields over finite fields from the viewpoint that the maximal cyclotomic extension of a number field is analogous to the constant field…

In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…