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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 …

Let $\chi_{s,k}$ be the characteristic function of integers $n$ which are expressed as sum of $s$ positive $k$-th powers i.e $\chi_{s,k}(n)=1$ if and only if $n=a_1^k+\cdots+a_s^k.$ Examples of this t …

Let $x$ be a sufficiently large number. Is there an explicit or asymptotic formula for the following sum $$\sum_{\substack{n\leq x\\ n=a^2+b^2+c^2}} 1.$$ Any reference would be helpful.

I want to write a survey on the subject 'Sign changes for coefficients of symmetric power $L$-functions'. So, I browse the Web and I got some papers. I read it and I gave special interest to the paper …

I am a graduate PhD student and my topic is analytic number theory. I am also a mathematics teacher. I am planning to give a course to pupils in high school that motivates them to study arithmetic and …

Let $f$ be an arithmetic function such that $f(n)\ll n^{\alpha}$ for some Real number $\alpha$ in $[0,1)$. Can someone give me examples of such functions other than the sum of divisors function or is …