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### q-series identities and values of certain L-functions

George E. Andrews, Jorge Jiménez-Urroz, and Ken Ono
Source: Duke Math. J. Volume 108, Number 3 (2001), 395-419.

#### Abstract

As usual, define Dedekind's eta-function η(z) by the infinite product

In a recent paper, D. Zagier proved that (note: empty products equal 1 throughout)

where the series D(q) and E(q) are defined by

Here d(n) denotes the number of positive divisors of n. We obtain two infinite families of such identities and describe some consequences for L-functions and partitions. For example, if χ2 is the Kronecker character for ℚ(), these identities can be used to show that

First Page:
Primary Subjects: 11F20
Secondary Subjects: 11B65
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091737179
Mathematical Reviews number (MathSciNet): MR1838657
Digital Object Identifier: doi:10.1215/S0012-7094-01-10831-4
Zentralblatt MATH identifier: 1005.11048

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