Some remarks on the coefficients of symmetric
                    power 𝐿-functions

Kumar, Balesh; Meher, Jaban; Pujahari, Sudhir

doi:10.1090/conm/732/14814

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“…Remark 1.4. The abscissa of absolute convergence of the series L(s, sym m f ) has been found out in [3]. But the method of proof of the same result is different in this paper.…”

Section: Introductionmentioning

confidence: 85%

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On the coefficients of symmetric power L-functions

Meher

Shankhadhar

Viswanadham

2018

Int. J. Number Theory

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Abstract. We study the signs of the Fourier coefficients of a newform. Let f be a normalized newform of weight k for Γ 0 (N ). Let a f (n) be the nth Fourier coefficient of f . For any fixed positive integer m, we study the distribution of the signs of {a f (p m )} p , where p runs over all prime numbers. We also find out the abscissas of absolute convergence of two Dirichlet series with coefficients involving the Fourier coefficients of cusp forms and the coefficients of symmetric power Lfunctions.

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“…Remark 1.4. The abscissa of absolute convergence of the series L(s, sym m f ) has been found out in [3]. But the method of proof of the same result is different in this paper.…”

Section: Introductionmentioning

confidence: 85%

“…But the method of proof of the same result is different in this paper. However, using the method of [3], one will not be able to find the abscissa of absolute convergence of the series L m (s, f ) for all integers m ≥ 1.…”

Section: Introductionmentioning

confidence: 99%