Abstract
Let rQ(n) be the representation number of a nonnegative integer n by a certain quinary quadratic form Q of level 8. Then the associated theta function is a modular form of weight 5/2 for Γ0(8) associated with the character (8⋅). We express this theta function as a linear combination of Hecke eigenforms and find the general formula of the representation number rQ(n). As a consequence, we show that rQ(n) satisfies some partially multiplicative relations by applying Fricke involution and Hecke operators on the associated theta functions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.