This paper considers theories of bounded arithmetic which are predicative in the sense of Nelson, that is, theories which are interpretable in Robinson’s Q . We give a nearly exact characterization of functions which can be total in predicative bounded theories. As an upper bound, any such function has polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-no...

Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the “Theory of Congruences” in Graph Theory, thus paved the way for the emergence of a new class of graphs, namely “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes an A...

We introduce the volume function for C-hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef C-hermitian invertible sheaf. We also give another applications, for example, a generalized Hodge ...

We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes, semi-stable arithmetic similarity classes, and well-rounded arithmetic similarity classes of bounded height as the bound tends to infinity. We also briefly discuss so...

This paper, first, we consider the Volterra integral equation for remainder term in asymptotic formula associated Euler totient function. Secondly, solve and split error function into two summands called arithmetic analytic part respectively.

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

The SNAP (Stanford Nanosecond Arithmetic Processor) project is targeted at realizing an arithmetic processor with performance approximately an order of magnitude faster than currently available technology. The realization of SNAP is predicated on an interdisciplinary approach and effort spanning research in algorithms, data representation, CAD, circuits and devices, and packaging. SNAP is visua...

• Innovative work by Kabanets and Impagliazzo [KI03] shows that, in some cases, providing lower bounds on arithmetic circuit size can yield consequences about Boolean complexity classes. For instance, one of the most important problems in BPP that is not known to be in P is Arithmetic Circuit Identity Testing (ACIT), the problem of determining if two arithmetic circuits compute the same functio...

In this paper, the authors provide several sharp upper and lower bounds for Neuman–Sándor mean in terms of arithmetic contra-harmonic means, present some new inequalities involving hyperbolic sine function cosine function.