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Voronoi-type identity for a class of arithmetical functions via the Laplace transform
We provide a simple proof of a Voronoi type identity using the Laplace transform for a class of arithmetical functions whose generating Dirichlet...
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A Calculus on Arithmetical Functions
The previous chapter introduced the concept of arithmetical convolution, unitary or otherwise, and the basics of a new type of calculus appeared. We...
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Group of Arithmetical Functions (Optional)
In this chapter, we show that the set of all arithmetical functions f with \(f(1)\not =0\)...
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Harmonic Analysis of Some Arithmetical Functions
We study three functions which are power series in the variable z, Dirichlet series in the variable s and with coefficients given by arithmetical...
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Growth of Arithmetical Functions
In this chapter, we prove pointwise upper bounds for the values of arithmetic functions. This question is crucial to evaluate the abscissa of...
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Arithmetical Rings
In this paper, some familiar and new results on arithmetical rings, modules, and Bezout rings (not necessarily commutative) are provided. In...
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Generalizations of Alladi’s formula for arithmetical semigroups
In this article, we prove that a general version of Alladi’s formula with Dirichlet convolution holds for arithmetical semigroups satisfying Axiom A ...
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Arithmetical Decidability of Homogeneous and Almost Prime Countable Models of Ehrenfeucht Theories with Arithmetical Types
We show that countable homogeneous and almost prime models of Ehrenfeucht theories with arithmetically decidable types are arithmetically decidable.
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Problems of Arithmetical Geometry
This chapter includes the theory of Ci-fields, Kronecker conjugacy of global field extensions, Davenport’s problem on value sets of polynomials over...
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A new arithmetical function and its mean value properties
In this article, we use elementary methods and the estimate for character sums to study the mean value properties of a new arithmetical function, and...
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A Survey on the Theory of Multiple Dirichlet Series with Arithmetical Coefficients as Numerators
We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients as numerators.
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Sign changes of certain arithmetical function at prime powers
We examine an arithmetical function defined by recursion relations on the sequence { f ( p k )} k ∈ℕ and obtain sufficient condition(s) for the sequence to...
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Remarks on the Number Theory Over Additive Arithmetical Semigroups
We deal with additive arithmetical semigroups and present old and new proofs for the distribution of zeros of the corresponding ζ-functions. We use...
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Investigating rational perfect nonlinear functions
Perfect nonlinear (PN) functions over a finite field, whose study is also motivated by practical applications to Cryptography, have been the subject...
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Primes in Arithmetical Progressions
We first gently steer the readers through the general notions and then inspect them more closely in two special cases.
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Martin–Löf reducibility and cost functions
Martin-Löf (ML)-reducibility compares the complexity of K -trivial sets of natural numbers by examining the Martin-Löf random sequences that compute...