Selected Publications

Selected Publications
C. Spiro, For the local distribution of the group-counting function, orders divisible by fifth powers can be neglected, submitted December 2011.

C. Spiro-Silverman, Groups of cubefree order, Acta Arith., LXXI 3. (1995), 209-227.

Divisibility of the -fold iterated divisor function of n into n, ACTA ARITHMETICA LXVIII.4 (1994), 307-339

C. Spiro, Additive Uniqueness Sets for Arithmetic Functions, J. Number Theory 42.2, October (1992), 232-246
C. Spiro-Silverman, When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently, Acta Arith. 61 (1992), 1-12.
With P. Erdös, A. Granville, and C. Pomerance, On the normal behavior of the iterates of some Arithmetic Functions, Analytic Number Theory: Procedings of a Conference in Honor of Paul T. Bateman, Birkhauser Boston, Inc. 1990

C. Spiro, The probability that the number of groups of squarefree order is two
more than a fixed prime, Proc. London Math. Soc. 60 (1990), 444–470.

C. Spiro, Local distribution results for the group-counting function at positive integers, Congressus Numerantium 50 (1985) 107-110

C. Spiro, An iteration problem involving the divisor function, Acta Arith. 46 (1986),
215–225. http://matwbn.icm.edu.pl/ksiazki/aa/aa46/aa4633.pdf

C. Spi ro, How often is the number of divisors of n a divisor of n?, J. Number
Theory 21 (1985), 81–100.X.

C. Spiro, Extensions of some formula of A. Selberg, Internat. J. Math. Math. Sci. 8
(1985), 283–302.

C.. Spiro, How Often Does the Number of Divisors of an Integer Divide Its Successor?, J. London Math. Soc. (1985) s2-31 (1): 30-40.

C. Spiro, The Frequency With Which an Integral-Valued, Prime-Independent, Multiplicative or Additive Function of n Divides a Polynomial Function of n, PhD Dissertation, University of Illinois at Urbana-Champaign, 1981. 188 pp.