Abstract
In this paper, we prove quantitative theorems for the number of sign changes for the sequences {λ(p)} and {λ(n)} where λ(n) are the normalised Hecke eigenvalues of the primitive holomorphic cusp form f. Also we prove quantitative theorem for the number of sign changes for the sequence {λ(n)} where λ(n) are the Hecke eigenvalues of a Maass cusp form f for the full modular group.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Chandrasekharan and R. Narasimhan, Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. of Math., (2) 76 (1962), 93–136.
J. Hoffstein and D. Ramakrishnan, Siegel zeros and cusp forms, Internat. Math. Res. Notices., (1995), no: 6, 279–308.
H. Iwaniec, Topics in classical automorphic forms, Amer.Math.Soc, 17, Providence RI, (1997).
H. Iwaniec, Spectral methods of automorphic forms, second edition, 53, Amer.Math.Soc, Providence, Rhode Island, Revista Matemática Iberoameri-cana (2002).
H. Iwaniec and E. Kowalski, Analytic Number theory, Amer.Math.Soc.Colloq.Publ., 53, AMS, Providence RI (2004).
A. Ivić, The Riemann zeta-function, Wiley (1985).
H.H. Kim and P. Sarnak, Refined estimates towards the Ramanujan and Selberg conjectures, Appendix 2 of the paper Functoriality for the exterior square of GL(4) and the symmetric fourth of GL(2) by H.H. Kim, J. Amer.Math.Soc, 1 16, 139–183 (2003).
W. Kohnen and J. Sengupta, On the first sign change of Hecke eigenvalues of newforms, Math.Z., 254 (2006), 173–184.
C.J. Moreno, The Hoheisel phenomenon for generalized Dirichlet series, Proc.Amer.Math.Soc, 40 (1973), 47–51.
M. Ram Murty, Oscillations of Fourier coefficients of modular forms, Math. Ann., 262 (1983), 431–446.
A. Sankaranarayanan, On Hecke L-functions associated with cusp forms-II (on the sign changes of S f (T)), Ann.Acad.Sci.Fenn.Math., 31 (2006), 213–238.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Hindustan Book Agency
About this chapter
Cite this chapter
Choie, Y.J., Sankaranarayanan, A., Sengupta, J. (2009). On the Sign Changes of Hecke Eigenvalues. In: Adhikari, S.D., Ramakrishnan, B. (eds) Number Theory and Applications. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-46-0_3
Download citation
DOI: https://doi.org/10.1007/978-93-86279-46-0_3
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-97-5
Online ISBN: 978-93-86279-46-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)