Divisor functions over quaternion algebras and a type of identities. (English) Zbl 1300.11119
Summary: In order to prove a result on fourth moments of modular \(L\)-functions, W. D. Duke [Commun. Pure Appl. Math. 41, No. 6, 815–831 (1988; Zbl 0659.10025)] derived an identity of the divisor function over the rational Hamiltonian quaternion algebra. Recently, H. H. Kim and the author [J. Number Theory 129, No. 12, 3000–3019 (2009; Zbl 1233.11118)] generalized Duke’s divisor function, the identity and other related results from level two to general prime level. In this note, we consider such identities in general.
MSC:
| 11R52 | Quaternion and other division algebras: arithmetic, zeta functions |
| 11N37 | Asymptotic results on arithmetic functions |
| 11R47 | Other analytic theory |
| 11F11 | Holomorphic modular forms of integral weight |
References:
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| [4] | H. H. Kim and Y. Zhang, Divisor function for quaternion algebras and application to fourth moments of L-functions , Journal of Number Theory, · Zbl 1233.11118 · doi:10.1016/j.jnt.2009.05.009 |
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