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Forbidden Integer Ratios of Consecutive Power Sums Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Multiplicative Functions and the Sign of Maass Form Fourier Coefficients

Author : Peter D. T. A Elliott

Published in: From Arithmetic to Zeta-Functions

Publisher: Springer International Publishing

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Abstract

Mean value theorems for multiplicative arithmetic functions are applied to demonstrate uniformity of sign changes in the Fourier coefficients of automorphic forms.

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previous chapter Sums of Two Squares and a Power
next chapter On Error Sum Functions for Approximations with Arithmetic Conditions
Literature
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T. Barnet-Lamb, D. Geraghty, M. Harris, R. Taylor, A family of Calabi-Yau varieties and potential automorphy II. Publ. Res. Inst. Math. Sci. 47 (1), 29–98 (2011)MathSciNetCrossRefMATH
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P.D.T.A. Elliott, Duality in Analytic Number Theory. Cambridge Tracts in Mathematics, vol. 122 (Cambridge University Press, Cambridge, 1997)
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P.D.T.A. Elliott, J. Kish, Harmonic analysis on the positive rationals I: basic results (2014). arXiv:1405.7130
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P.D.T.A. Elliott, J. Kish, Harmonic analysis on the positive rationals II: multiplicative functions and Maass forms (2014). arXiv:1405.7132
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H. Heilbronn, E. Landau, Anwendungen der N. Wienerschen Methode. Math. Z. 37 (1), 18–21 (1933); c.f. The Collected Papers of Hans Arnold Heilbronn, ed. by E.J. Kari, R.A. Smith. Canadian Mathematical Society Series of Monographs and Advanced Texts (Wiley, New York, 1988)
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H. Heilbronn, E. Landau, Bemerkungen zur vorstehenden Arbeit von Herrn Bochner. Math. Z. 37 (1), 10–16 (1933); c.f. The Collected Papers of Hans Arnold Heilbronn, ed. by E.J. Kari, R.A. Smith. Canadian Mathematical Society Series of Monographs and Advanced Texts (Wiley, New York, 1988)
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W. Schwarz, Some highlights from the history of probabilistic number theory, in Probability and Number Theory, Proceedings of the International Conference on Probability and Number Theory, Kanazawa, June 20–24, 2005, ed. by S. Akiyama, K. Matsumoto, L. Murata, H. Sugita. Advanced Studies in Pure Mathematics, vol. 49 (Mathematical Society of Japan, Tokyo, 2007), pp. 367–419
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W. Schwarz, J. Spilker, Arithmetical Functions. London Mathematical Society Lecture Note Series, vol. 184 (Cambridge University Press, Cambridge, 1994)
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E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen. II. Acta Math. Acad. Sci. Hung. 18, 411–467 (1967)MathSciNetCrossRefMATH
Metadata
Title
Multiplicative Functions and the Sign of Maass Form Fourier Coefficients
Author
Peter D. T. A Elliott
Copyright Year
2016
Book
From Arithmetic to Zeta-Functions

Print ISBN: 978-3-319-28202-2

Electronic ISBN: 978-3-319-28203-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-28203-9_8

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