On a r – GCD-Sum Function Over r-Regular Integers Modulo n r
V. Siva Rama Prasad1, P. Anantha Reddy2, M.Ganeshwar Rao3

1Dr. V. Siva Rama Prasad, Nalla Malla Reddy Engineering College Divyanagar, Kachivanisingaram (PO), Ghatkesar Mandal, R.R.District, Andhra Pradesh, INDIA.
2P.Anantha Reddy, Government Polytechnic, Vikarabad, R.R.District, Andhra Pradesh, INDIA.
3M.Ganeshwar Rao, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad, Andhra Pradesh, INDIA.
Manuscript received on February 04, 2013. | Revised Manuscript received on February 26, 2013. | Manuscript published on March 05, 2013. | PP: 7-11 | Volume-3 Issue-1, March 2013. | Retrieval Number: A1259033113/2013©BEIESP
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Abstract: Introducing an r-gcd-sum function over r-regular integers modulo , r n (studied by the authors [10] earlier), we obtain an asymptotic formula for its summatory function. The case r =1 of our result gives the formula established by László Tóth [8].
Keywords: R -regular integers modulo , r n r -gcd of two positive integers, n r , -residue system, reduced n r , – residue system, unitary divisor of an integer, Dirichlet divisor problem, Riemann Hypothesis. 2010 Mathematics Subject Classification: Primary: 11A25, Secondary: 11N37