Lower order terms for the one-level densities of symmetric power L-functions in the level aspect

Guillaume Ricotta; Emmanuel Royer

Displaying similar documents to “Lower order terms for the one-level densities of symmetric power L-functions in the level aspect”

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Mark van Hoeij (2002)

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Let L(y) = 0 be a linear differential equation with rational functions as coefficients. To solve L(y) = 0 it is very helpful if the problem could be reduced to solving linear differential equations of lower order. One way is to compute a factorization of L, if L is reducible. Another way is to see if an operator L of order greater than 2 is a symmetric power of a second order operator. Maple contains implementations for both of these. The next step would be to see if L is a symmetric...

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A positive integer n is called E-symmetric if there exists a positive integer m such that |m-n| = (ϕ(m),ϕ(n)), and n is called E-asymmetric if it is not E-symmetric. We show that there are infinitely many E-symmetric and E-asymmetric primes.