Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a problem of Arnold: the average multiplicative order of a given
  integer   For g,n coprime integers, let l_g(n) denote the multiplicative order of g
modulo n. Motivated by a conjecture of Arnold, we study the average of l_g(n)
as n <= x ranges over integers coprime to g, and x tending to infinity.
Assuming the Generalized Riemann Hypothesis, we show that this average is
essentially as large as the average of the Carmichael lambda function. We also
determine the asymptotics of the average of l_g(p) as p <= x ranges over
primes.

30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org