Explicit Upper Bounds for the Average Order of $d_{n}(m)$ and Application to Class Number

Volume 3, Issue 3, 2002

Article 38

EXPLICIT UPPER BOUNDS FOR THE AVERAGE ORDER OF d_n(m) AND APPLICATION TO CLASS NUMBER

22, RUE JEAN BARTHÉLEMY,
43000 LE PUY-EN-VELAY, FRANCE
E-Mail: borde43@wanadoo.fr

Received 29 June, 2001; Accepted 13 March, 2002.
Communicated by: J. Sándor

ABSTRACT. In this paper, we prove some explicit upper bounds for the average order of the generalized divisor function, and, according to an idea of Lenstra, we use them to obtain bounds for the class number of number fields.

Key words:
Multiplicative number theory, Average order, Class number.

2000 Mathematics Subject Classification:
11N99, 11R29.

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