Here is an article to solve the algebraic equation with degree above 4
For example, $t^5=a$, we get one solution to the equation: $$t=e^{\frac{1}{n}\int^a_1 \frac{1}{x}}$$, generalizing this result by replacing the exponential with Siegel modular function and the integral with hyperelliptic integrals, we can get every solution to an algebraic equation with degree above 5 formulated by Siegel modular function and hyperelliptic integrals, please see David Mumford Tate lecture on Theta $\textrm{II}$ Jacobian page 266 for more detail .
Could anyone write down the formula of the solution formulated by Siegel modular function and hyperelliptic integrals(or by other modular function and hyperelliptic integrals)? I think it may be like $$x= \lambda^{\int \frac{x^i}{\sqrt{F(x)}}dx}$$ where $\lambda$ is the Siegel modular function( I do not know it's form, please write it down)
Now Could we extend this result to algebraic equation like $$p_0(x) + p_1(x) \cdot y + p_2(x)\cdot y^2 + \cdots + p_n(x)\cdot y^n $$ with coefficients of $p_i(x) \in Q[x]$ to have solutions of $y$ which is the counterpart of $x$ in $a_0+a_1x+a_2x^2+\cdots+a_nx^n=0$ in the article($a_i$ is the counterpart of $p_i(x)$)?