3 problems

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Standard analytic properties conjecture for twisted symmetric-power L-functions
Let $k$ , $q$ , and $N$ be positive integers with $N$ squarefree, $k$ even, and $\gcd(N,q)=1$ . Let $f\in S_k^{\mathrm{new}}(\Gamma_0(N))$ be a non-CM newform, and let $\chi$ be a pri…
Conjectureopenautomorphic-forms generalized-riemann-hypothesis symmetric-power-l-functionsarXiv posted 2 days ago
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Montgomery–Vaughan's first conjecture for symmetric power $L$ -functions
Let $m$ be a fixed integer, and let $F_{k,N}^{\pm}(t,\operatorname{sym}^m)$ denote the distribution function of the values $L(1,\operatorname{sym}^m f)$ over…
Conjectureopenanalytic-number-theory automorphic-forms symmetric-power-l-functionsarXiv posted 2 days ago
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The symmetric-power conjecture for non-CM elliptic curves
Symmetric-power conjecture. For every $k\geq0$ , the conductor of $L(s,\operatorname{Sym}^k E)$ is $N_E^k$ ; its gamma factor is
Conjectureopenelliptic-curves generalized-riemann-hypothesis symmetric-power-l-functionsarXiv posted 2 days ago

Standard analytic properties conjecture for twisted symmetric-power L-functions