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Results tagged with automorphic-forms
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user 76102
An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.
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How to construct the symmetric power function from a modular form?
I want to understand how we construct from a modular form $f$ its symmetric power function $Sym^rf.$ I read that there is a particular representation that does this but I am not familiar with this no …
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Fourier expansion of automorphic forms
we know that for $r \in \{1,2,3,4\},$ $\lambda_{Sym^rf}$ is an automorphic form (here $f$ is a modular form for the full modular group) and this fact is conjectured for $r\geq 5$ by Langlands and Serr …
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Question about mean square estimate for sums of Dirichlet coefficients of Symmetric Power $L...
I have a question related to Coefficients of Symmetric power $L$-functions and I would be grateful if you could answer it.
Let $\lambda_{Sym^rf}(n)$ be the $n$th Dirichlet coefficient of $L(Sym^rf,s). …
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Shifted convolution problem for Coefficients of automorphic forms
The shifted convolution problem for coefficients of modular forms is well studied and many estimates were established for the shifted convolution sums of Hecke eigenvalues. So, one may ask about the g …
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