Linear quantum addition rules
Melvyn B. Nathanson
Abstract
The quantum integer [n]q is the polynomial 1 + q + q2 + ... + qn-1. Two sequences of polynomials U = \un(q)\n=1∞ and V = \vn(q)\n=1∞ define a linear addition rule on a sequence F = \fn(q)\n=1∞ by fm(q) fn(q) = un(q)fm(q) + vm(q)fn(q). This is called a quantum addition rule if [m]q [n]q = [m+n]q for all positive integers m and n. In this paper all linear quantum addition rules are determined, and all solutions of the corresponding functional equations fm(q) fn(q) = fm+n(q) are computed.
Create a lesson
Related papers
Value distribution of multiplicative functions along linear fractional sequences
Sun-Kai Leung
Delta theory of Anderson Modules II: Hodge-Pink structure
Sudip Pandit, Arnab Saha
Integers divisible by a shifted prime in a given interval
Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt et al.
On Piatetski-Shapiro primes from almost primes
Yuhua Zhao, Jinjiang Li, Linji Long et al.
On Consecutive Non-primitive Elements over Finite Fields
Bidushi Sharma, Dhiren Kumar Basnet
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu