On multiplicative functions with f(p+q+n0)=f(p)+f(q)+f(n0)
نویسندگان
چکیده
منابع مشابه
Arithmetical Functions I: Multiplicative Functions
Truth be told, this definition is a bit embarrassing. It would mean that taking any function from calculus whose domain contains [1,+∞) and restricting it to positive integer values, we get an arithmetical function. For instance, e −3x cos2 x+(17 log(x+1)) is an arithmetical function according to this definition, although it is, at best, dubious whether this function holds any significance in n...
متن کاملMultiplicative Functionals on Semigroups of Continuous Functions
Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...
متن کاملMultiplicative character sums with twice-differentiable functions
For a nontrivial multiplicative character χ modulo p, we bound character sums Sf (χ;N) = N ∑ n=1 χ(⌊f(n)⌋) taken on the integer parts of a real-valued, twice-differentiable function f whose second derivative decays at an appropriate rate. For the special case that f(x) = xη with some positive real number η, our bounds extend recent results of several authors. Mathematics Subject Classification ...
متن کاملMultiplicative Distance Functions
We call φ the root function of Φ. The continuity of Φ implies that (1.2) φ(γ) → |γ| as |γ| → ∞. Moreover the converse is true, if φ is continuous and satisfies this asymptotic formula, then the function Φ formed as in (1.1) is a multiplicative distance function. Theorem 1.1. A continuous function φ : C → [0,∞) is the root function of a multiplicative distance function iff it satisfies (1.2). Ar...
متن کاملCompletely Multiplicative Automatic Functions
We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.01.027