1 The classical Möbius function 1.1 Arithmetic functions and Dirichlet series. Write N (meant to encode some arithmetic feature of each number n). To each arithmetic function f one associates a Dirichlet series F (s) = n≥1 f (n) n s thought of as a function defined on some open set of the complex plane. Analytic number theory is to a large extent the study of arithmetic functions in terms of th...

Abstract In the last few years, number of applications multidimensional fuzzy arithmetic (MFA) and interval is expanding. Authors new papers about MFA are often faced with comments from other researchers, especially gradual (GA) proponents, that horizontal membership function (HMF) used in same as inverse (InvMF) GA, itself adds nothing to arithmetic. This view leads unfair evaluations scientif...

This paper is the sequel of the paper [4], in which we established the arithmetic volume function of C-hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume function has a lot of applications as treated in [4]. In this paper, we would like to consider its continuous extension over R. CONTENTS Introduction 1 1. A multi-indexed version of the fundamental estimatio...

Elementary arithmetic (also known as “elementary function arithmetic”) is a fragment of first-order arithmetic so weak that it cannot prove the totality of an iterated exponential function. Surprisingly, however, the theory turns out to be remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and ...