Geodesic
Arithmetic properties of Shimura sums related to several modular forms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 7-22

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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. 
@article{FPM_2010_16_6_a1,
     author = {G. V. Voskresenskaya},
     title = {Arithmetic properties of {Shimura} sums related to several modular forms},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {7--22},
     publisher = {mathdoc},
     volume = {16},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a1/}
}
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G. V. Voskresenskaya. Arithmetic properties of Shimura sums related to several modular forms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 6, pp. 7-22. http://geodesic.mathdoc.fr/item/FPM_2010_16_6_a1/