FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 6, PAGES 7-22

**Arithmetic properties of Shimura sums related to several modular forms**

G. V. Voskresenskaya

Abstract

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The paper is concerned with Shimura sums related to modular forms
with multiplicative coefficients which are products of Dedekind
$$h-functions of various
arguments.
Several identities involving Shimura sums are established.
The type of an identity obtained depends on the splitting of primes in
certain imaginary quadratic number fields.

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Last modified: July 5, 2011