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Consecutive Large Gaps in Sequences Defined by Multiplicative Constraints

Published online by Cambridge University Press:  20 November 2018

Emre Alkan  and
Alexandru Zaharescu
Emre Alkan
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A. e-mail: [email protected]
Alexandru Zaharescu
Affiliation:
Department of Mathematics, Koc University, 34450 Sariyer, Istanbul, Turkey e-mail: [email protected]
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Abstract

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In this paper we obtain quantitative results on the occurrence of consecutive large gaps between $B$-free numbers, and consecutive large gaps between nonzero Fourier coefficients of a class of newforms without complex multiplication.

Keywords

11N2511B05B-free numbersconsecutive gaps
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 172 - 181
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Alkan, E., Nonvanishing of Fourier coefficients of modular forms. Proc. Amer. Math. Soc. 131(2003), no. 6, 1673–1680.Google Scholar
[2] Alkan, E., On the sizes of gaps in the Fourier expansion of modular forms. Canad. J. Math. 57(2005), no. 3, 449–470.Google Scholar
[3] Alkan, E. and Zaharescu, A., B-free numbers in short arithmetic progressions. J. Number Theory 113(2005), no. 2, 226–243.Google Scholar
[4] Alkan, E. and Zaharescu, A., Nonvanishing of Fourier coefficients of newforms in progressions. Acta Arith. 116(2005), no. 1, 81–98.Google Scholar
[5] David, C. and Pappalardi, F., Average Frobenius distributions of elliptic curves. Internat. Math. Res. Notices 1999, no. 4, 165–183.Google Scholar
[6] Erdőos, P., On the difference of consecutive terms of sequences defined by divisibility properties. Acta Arith. 12(1966/1967), 175–182.Google Scholar
[7] Fouvry, E. and Murty, M. R., On the distribution of supersingular primes. Canad. J. Math. 48(1996), no. 1, 81–104.Google Scholar
[8] Halberstam, H. and Richert, H.-E., Sieve methods. London Mathematical Society Monographs 4, Academic Press, London, 1974.Google Scholar
[9] Kowalski, E., Robert, O., and Wu, J., Small gaps in coefficients of L-functions and -free numbers in small intervals. Rev. Mat. Iberoam. 23(2007), no. 1, 281–326.Google Scholar
[10] Murty, M. R., Recent developments in elliptic curves. In: Proceedings of the Ramanujan Centennial International Conference. RMS Publ. 1, Ramanujan Math. Soc., Annamalainagar, 1988, pp. 45–53.Google Scholar
[11] Murty, V. K., Frobenius distributions and Galois representations. In: Automorphic Forms, Automorphic Representations, and Arithmetic. Proc. Sympos. Pure Math. 66, American Mathematical Society, Providence, RI, 1999, pp. 193–211.Google Scholar
[12] Panaitopol, L., On square free integers. Bull. Math. Soc. Sci. Math. Roumanie 43(91)(2000), no. 1, 19–23.Google Scholar