Summation of the euler function values over numbers of the form p − 1

Moscow University Mathematics Bulletin - Tập 64 - Trang 41-43 - 2009
D. V. Goryashin1
1Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

Tóm tắt

An asymptotic formula is proved for the sum of values of the Euler function on numbers of the form p − 1 not exceeding x. The order of the remainder of the asymptotics corresponds to the modern bound for zeros of the zeta function.

Tài liệu tham khảo

A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971) [in Russian]. A. A. Karatsuba, Basic Analytic Number Theory, 2nd ed. (Nauka, Moscow, 1983; Springer, 1992). G. I. Arkhipov, V. A. Sadovnichii, and V. N. Chubarikov, Lectures in Mathematical Analysis, 3rd ed. (Drofa, Moscow, 2003) [in Russian].