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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