Abstract
In this article, we investigate the sign changes of the sequence of coefficients at sum of two squares where the coefficients are the Fourier coefficients of the normalized Hecke eigen cusp form for the full modular group. We provide the quantitative result for the number of sign changes of the sequence in a small interval.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bump D, The Rankin–Selberg Method: A Survey, Number Theory, Trace Formulas and Discrete Groups (1989) (Boston: Academic Press) pp. 49–109
Deligne P, La Conjecture de Weil, I, Inst. Hautes Etudes Sci. Publ. Math. 43 (1974) 273–307
Gun S and Sengupta J, Sign changes of Fourier coefficients of Siegel cusp forms of degree two on Hecke congruence subgroups, Int. J. Number Theory 13(10) (2017) 2597–2625
Iwaniec H, Topics in Classical Automorphic Forms, Grad. Stud. Math., vol. 17, (1997) (Providence, RI: American Mathematical Society)
Iwaniec H and Kowalski E, Analytic Number Theory, Amer. Math. Soc. Colloquium Publ. 53 (2004) (Providence, RI: Amer. Math. Soc.)
Knopp M, Kohnen W and Pritbikin W, On the signs of Fourier coefficients of cusp forms, Ramanujan J. 7 (2003) 269–277
Kohnen W and Martin Y, Sign changes of Fourier coefficients of cusp forms supported on prime power indices, Int. J. Number Theory 10(8) (2014) 1921–1927
Kohnen W, Lau Yuk-Kam and Shparlinski Igor E, On the number of sign changes of Hecke eigenvalues of newforms, J. Aust. Math. Soc. 85(1) (2008) 87–94
Kohnen W and Sengupta J, On the first sign change of Hecke eigenvalues of newforms, Math. Z. 254 (2006) 173–184
Lao H and Sankaranarayanan A, The average behaviour of Fourier coefficients of cusp forms over sparse sequences, Proc. Amer. Math. Soc. 8 (2009) 2557–2565
Matsumoto K, The mean-values and the universality of Rankin–Selberg L-functions, Number Theory (Turku, 1999) (2001) (Berlin: de Gruyter) pp. 201–221
Meher J and Ram Murty M, Oscillations of coefficients of Dirichlet series attached to automorphic forms, Proc. Amer. Math. Soc. 145(2) (2017) 563–575
Meher J, Shankhadhar K and Viswanadham G K, A short note on sign changes, Proc. Indian Acad. Sci. (Math. Sci. )123 (2013) 315–320
Ram Murty M, Oscillations of the Fourier coefficients of Modular forms, Math. Ann. 262 (1983) 431–446
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: Sanoli Gun
Rights and permissions
About this article
Cite this article
Banerjee, S., Pandey, M.K. Signs of Fourier coefficients of cusp form at sum of two squares. Proc Math Sci 130, 2 (2020). https://doi.org/10.1007/s12044-019-0534-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12044-019-0534-4