A case of simultaneous non-vanishing
classification
🧮 math.NT
keywords
caseevenexistslargelevelnewformnon-vanishingnumber
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We show that for $k>1000$ an even number and a sufficiently large prime $q$, there exists a newform $f$ of weight $k$ and level $q$ such that $$ L(1/2,f)L(1/2,\text{Sym}^2 f)\neq 0. $$
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