Geodesic
Some Analytic Methods with Applications to Number Theory
Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 21 .

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We study the arithmetical function ``exponent (order) of an integer modulo m" which is here shortly named ``period" of m. A method is developed, named ``separation of parameters", that leads to analytic representation of the function period. Though Bessel functions have dominant role, other special functions are also applicable. The most promising result is derived by making use of Mukisi\'nski's concept of distributions. The developed method, besides its general nature, makes it possible to study computability of arithmetical function period by means of analytic procedures.
Classification : 10-20 10H25 33A40 10K20 46F99
Keywords: Exponent (order) of an integer modulo $m$, distribution Mersenne and Fermat primes, special functions, Bessel functions, interpolation, Bernoulli and Euler polynomials 
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     author = {Dimitrije Ugrin-\v{S}parac},
     title = {Some {Analytic} {Methods} with {Applications} to {Number} {Theory}},
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Dimitrije Ugrin-Šparac. Some Analytic Methods with Applications to Number Theory. Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 21 . http://geodesic.mathdoc.fr/item/PIM_1987_N_S_41_55_a2/