Arithmetic properties of Shimura sums related to several modular forms

G. V. Voskresenskaya

Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 7-22.

Résumé

The paper is concerned with Shimura sums related to modular forms with multiplicative coefficients which are products of Dedekind $\eta$-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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