Multiplicative functions and Ramanujan's τ-function
نویسندگان
چکیده
منابع مشابه
Pretentious Multiplicative Functions and an Inequality for the Zeta-Function
We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions f that pretend to be another multiplicative function g. We formalize a ‘distance’ which gives a measure of such pretentiousness, and as one consequence obtain a curious inequality for the zeta-function. A common theme in several problems in multiplicative number th...
متن کاملPfaff Τ -functions
6 Examples 32 6.1 Symmetric matrix integrals . . . . . . . . . . . . . . . . . . . 33 6.2 Quasiperiodic solutions . . . . . . . . . . . . . . . . . . . . . . 34 Department of Mathematics, Brandeis University, Waltham, Mass 02454, USA. Email: [email protected]. The support of a National Science Foundation grant # DMS-98-4-50790 is gratefully acknowledged. Department of Mathematics, Kyoto U...
متن کاملArithmetical 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 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 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 the Australian Mathematical Society
سال: 1981
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700017936