Abstract
We show that the methods of Motohashi and Meurman yield the same upper bound on the error term in the binary additive divisor problem. To this end, we improve an estimate in the proof of Motohashi.
Similar content being viewed by others
References
J.-M. Deshouillers and H. Iwaniec, “An additive divisor problem,” J. London Math. Soc., Ser. 2, 26, 1–14 (1982).
T. Estermann, “Über die Darstellungen einer Zahl als Differenz von zwei Produkten,” J. Reine Angew. Math. 164, 173–182 (1931).
D. R. Heath-Brown, “The fourth power moment of the Riemann zeta function,” J. London Math. Soc., Ser. 3, 38, 385–422 (1979).
A. E. Ingham, “Some asymptotic formulae in the theory of numbers,” J. London Math. Soc. 2, 202–208 (1927).
H. H. Kim (with appendix 1 by D. Ramakrishnan and appendix 2 by H. H. Kim and P. Sarnak), “Functoriality for the exterior square of GL 4 and the symmetric fourth of GL 2,” J. Am. Math. Soc. 16, 139–183 (2003).
N. V. Kuznetsov, “Petersson’s conjecture for cusp forms of weight zero and Linnik’s conjecture. Sums of Kloosterman sums,” Mat. Sb. 111 (3), 334–383 (1980) [Math. USSR, Sb. 39 (3), 299–342 (1981)].
N. V. Kuznetsov, “Convolution of the Fourier coefficients of the Eisenstein–Maass series,” Zap. Nauchn. Semin. LOMI 129, 43–84 (1983) [J. Sov. Math. 29 (2), 1131–1159 (1985)].
T. Meurman, “On the binary additive divisor problem,” in Number Theory: Proc. Turku Symp. on Number Theory in Memory of Kustaa Inkeri, Turku, 1999, Ed. by M. Jutila et al. (W. de Gruyter, Berlin, 2001), pp. 223–246.
Y. Motohashi, “Spectral mean values of Maass waveform L-functions,” J. Number Theory 42 (3), 258–284 (1992).
Y. Motohashi, “The binary additive divisor problem,” Ann. Sci. Éc. Norm. Supér., Sér. 4, 27 (5), 529–572 (1994).
NIST Handbook of Mathematical Functions, Ed. by F.W. J.Olver,D.W. Lozier, R.F. Boisvert, and C. W. Clarke (Cambridge Univ. Press, Cambridge, 2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 50–55.
Rights and permissions
About this article
Cite this article
Balkanova, O.G., Frolenkov, D.A. On the Binary Additive Divisor Problem. Proc. Steklov Inst. Math. 299, 44–49 (2017). https://doi.org/10.1134/S0081543817080028
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543817080028