Discrete mean square of the coefficients of symmetric square L-functions on certain sequence of positive numbers

Sharma, A.; Sankaranarayanan, A.

doi:10.1007/s40993-022-00319-8

Cited by 8 publications

(1 citation statement)

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“…For such divisor problems connected to holomorphic cusp forms, see the work of H.F. Liu [Liu18], [LiuZha19] and Lü [Lü12]. Recently, several authors considered the average behavior of λ sym j f (n) over certain sequences of positive integers and established some interesting asymptotic formulas (see, for instance [ShSa22a,ShSa22b,ShSa22c,Hua22]).…”

Section: Introductionmentioning

confidence: 99%

On a general divisor problem related to a certain Dedekind zeta-function over a specific sequence of positive integers

Sharma,

Sankaranarayanan

2024

Hardy-Ramanujan Journal

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We investigate the average behavior of coefficients of the Dirichlet series of positive integral power of the Dedekind zeta-function $\zeta_{\mathbb{K}_3}(s)$ of a non-normal cubic extension $\mathbb{K}_3$ of $\mathbb{Q}$ over a certain sequence of positive integers. More precisely, we prove an asymptotic formula with an error term for the sum\[ \sum_{{a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}\leq {x}}\atop{(a_{1},a_{2},a_{3},a_{4},a_{5},a_{6})\in\mathbb{Z}^{6}}}a_{k,\mathbb{K}_3} (a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}),\]where $(\zeta_{\mathbb{K}_3}(s))^{k}:=\sum_{n=1}^{\infty}\frac{a_{k,\mathbb{K}_3}(n)}{n^{s}}$.

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