Arithmetic Function Interpreter in C# 3.0 Using Lambda Expression Trees.

AbstractLet Sk(Γ) be the space of holomorphic cusp forms of even integral weight k for the full modular group SL(z, ℤ). Let be the n-th normalized Fourier coefficients of three distinct holomorphic primitive cusp forms , and h(z) ∊ Sk3 (Γ), respectively. In this paper we study the cancellations of sums related to arithmetic functions, such as twisted by the arithmetic function λf(n).

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Note on the distribution of values of the arithmetic function $d\left( m \right)$

Bulletin of the American Mathematical Society ◽

10.1090/s0002-9904-1941-07575-0 ◽

1941 ◽

Vol 47 (10) ◽

pp. 815-818 ◽

Cited By ~ 5

Author(s):

M. Kac

Keyword(s):

Arithmetic Function ◽

Distribution Of Values

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A Note on Dirichlet Convolutions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1966-055-8 ◽

1966 ◽

Vol 9 (4) ◽

pp. 457-462

Author(s):

S. L. Segal

Keyword(s):

Arithmetic Function ◽

General Theorem ◽

Möbius Function ◽

Order Condition ◽

Mobius Function

In [3] Rubel proved that if h(n) is an arithmetic function such that , L finite, then where μ(n) is the Mobius function. This result was extended to functions other than μ(n) in [4]; however, (as first pointed out to the author by Benjamin Volk), the order condition imposed there is unnecessary; in fact, utilizing the result of [3], the following slightly more general theorem has an almost trivial proof.

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Footnote to a Formula of Gioia and Subbarao

Canadian Mathematical Bulletin ◽

10.4153/cmb-1967-080-6 ◽

1967 ◽

Vol 10 (5) ◽

pp. 749-750

Author(s):

S. L. Segal

Keyword(s):

Explicit Formula ◽

Arithmetic Function ◽

Fixed Integer ◽

Simple Idea ◽

Image Position ◽

Multiplicative Formula

Recently Gioia and Subbarao [2] studied essentially the following problem: If g(n) is an arithmetic function, and , then what is the behaviour of H(a, n) defined for each fixed integer a ≥ 2 by1By using Vaidyanathaswamy′s formula [e.g., 1], they obtain an explicit formula for H(a, n) in case g(n) is positive and completely multiplicative (Formula 2.2 of [2]). However, Vaidyanathaswamy′s formula is unnecessary to the proof of this result, which indeed follows more simply without its use, by exploiting a simple idea used earlier by Subbarao [3] (referred to also in the course of [2]).

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Some Identities on the Poly-Genocchi Polynomials and Numbers

Symmetry ◽

10.3390/sym12061007 ◽

2020 ◽

Vol 12 (6) ◽

pp. 1007 ◽

Cited By ~ 4

Author(s):

Dmitry V. Dolgy ◽

Lee-Chae Jang

Keyword(s):

Arithmetic Function ◽

Bernoulli Polynomials ◽

Genocchi Polynomials

Recently, Kim-Kim (2019) introduced polyexponential and unipoly functions. By using these functions, they defined type 2 poly-Bernoulli and type 2 unipoly-Bernoulli polynomials and obtained some interesting properties of them. Motivated by the latter, in this paper, we construct the poly-Genocchi polynomials and derive various properties of them. Furthermore, we define unipoly Genocchi polynomials attached to an arithmetic function and investigate some identities of them.

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