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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

1 vote
1 answer
173 views

Is this function concave or convex? [closed]

let $g_{n,\gamma}(\sigma)$ be the function defined as the following $$ g_{n,\gamma}(\sigma)= \left(\frac{(\sigma-1)^2 +\gamma^2}{\sigma^2 +\gamma^2} \right)^{n/2} T_n\left( \frac{\sigma(\sigma-1) +\g …
Khadija Mbarki's user avatar
0 votes
0 answers
80 views

Comparison of two functions

Given a function $f$ from $R^2$ to $R$ satisfying tha following: $1)$ $f$ is a convex function which vanishes on $(0,1)$ and on $(1,0).$ $2)$ $f$ is a decreasing function on $x$ and on $y$ and $f …
Khadija Mbarki's user avatar
0 votes
1 answer
125 views

Discussion for the sign of a specific sum

Given a modular form $f$ of an even weight $k$ for the full modular group. Let $\lambda_f(n)$ the $n$-th normalized Fourier coefficient of $f.$ For a fixed positive integers $a$ and $b,$ I want to dis …
Khadija Mbarki's user avatar
1 vote
Accepted

Discussion for the sign of a specific sum

Using The Euler product, we can express the sum $$\sum_{\substack{l=1\\\gcd(l,a)=\gcd(l,b)=1}}^{+\infty}\left(\frac{\lambda_f(l)}{l^{3/4}}\right)^3$$ as an infinite product over prime numbers so that …
Khadija Mbarki's user avatar