Abstract
The 1916 memoir of Ramanujan modestly entitled “On certain arithmetic functions” contains a wealth of ideas. Most notable is the study of what is now called Ramanujan’s τ-function. In this chapter, we discuss the basic properties of this function as well as highlight some theorems and conjectures regarding its values.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-81-322-0770-2_13
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References
J. Bruinier, K. Ono, R. Rhoades, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues. Math. Ann. 342(3), 673–693 (2008)
D.H. Lehmer, Ramanujan’s function τ(n). Duke Math. J. 10, 483–492 (1943)
D.H. Lehmer, The vanishing of Ramanujan’s function τ(n). Duke Math. J. 14, 429–433 (1947)
N. Lygeros, O. Rozier, A new solution to the equation τ(p)≡0 (mod p). J. Integer Seq. 13(7) (2010). Article 10.7.4, 11 pp
M.R. Murty, Oscillations of Fourier coefficients of modular forms. Math. Ann. 262, 431–446 (1983)
M.R. Murty, V.K. Murty, T.N. Shorey, Odd values of the Ramanujan τ-function. Bull. Soc. Math. Fr. 115(3), 391–395 (1987)
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Murty, M.R., Murty, V.K. (2013). The Ramanujan τ-Function. In: The Mathematical Legacy of Srinivasa Ramanujan. Springer, India. https://doi.org/10.1007/978-81-322-0770-2_2
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DOI: https://doi.org/10.1007/978-81-322-0770-2_2
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