Related papers: A residue scalar product for algebraic function fi…

In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the…

In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…

We formulate for function fields an analog of Serre's conjecture on the modularity of 2-dimensional irreducible mod l representations of the absolute Galois group of Q: our analog is not restricted to 2-dimensional represntations. While the…

We obtain closed form of some infinite series involving derivatives of an analogue of the Riemann xi function for Dedekind zeta function and nontrivial zeros of Dedekind zeta function assuming the Extended Riemann Hypothesis. Conversely, we…

We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems…

This paper studies the function field of an algebraic curve over an arbitrary perfect field by using the Weil reciprocity law and topologies on the adele ring. A topological subgroup of the idele class group is introduced and it is shown…

In this paper we present a detailed proof of an important result of algebraic logic: namely that the free commutative Kleene algebra is the space of semilinear sets. The first proof of this result was proposed by Redko in 1964, and…

This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998…

We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums…

In this paper we will give an explicit construction of the geometric model for a prescribed extension of a function field in several variables over a number field. As a by-product, we will also prove the existence of quasi-galois closed…

In the 1950s and 1960s Tate proved some duality theorems in the Galois cohomology of finite modules and abelian varieties. As for most of Tate's work this has had a profound influence on mathematics with many applications and further…

In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of the Mellin transform. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the…

UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete…

It is shown that a valuation of residue characteristic different from $2$ and $3$ on a field $E$ has at most one extension to the function field of an elliptic curve over $E$, for which the residue field extension is transcendental but not…

We construct a vector field E from the real and imaginary parts of an entire function xi (z) which arises in the quantum statistical mechanics of relativistic gases when the spatial dimension d is analytically continued into the complex z…

In this paper, authors prove that if $X$ is a weak Asplund space, then the space $X\times R$ is a weak Asplund space. Thus the author definitely answered an open problem raised by D.G. Larman and R.R. Phelps for 45 years ago (J. London.…

In 1931, Banach proved that, far from being exceptional objects, the Weierstrass functions form a residual set in the space $\mathcal{C}[0,1]$ of continuous functions. Later on, in 1966, V. I. Gurariy showed that, except for zero, there is…

As an application of P. Delgine's theorem (Esnault and Kerz in Acta Math. Vietnam. 37:531-562, 2012) on a finiteness of $l$-adic sheaves on a variety over a finite field, we show the finiteness of \'etale coverings of such a variety with…

Just as a residue field can be considered for a point of an algebraic variety, we can also consider a residue field for a point of a Berkovich analytic space. This residue field is a valuation field in the algebraic sense. Then we can…

Building on work of Kuhlmann and Lisinski, we study the theory of the Hahn series field $\mathbb{F}_{q}(\!(\mathbb{Q})\!)$, over a finite field $\mathbb{F}_{q}$, equipped with the $t$-adic valuation, in a language of valued fields. We prove…