Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896860 | Journal of Number Theory | 2018 | 23 Pages |
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 Î0(8) associated with the character (8â
). 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ick Sun Eum,