1. Sign changes of coefficients and sums of coefficients of L-functions.
- Author
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Hulse, Thomas A., Ieong Kuan, Chan, Lowry-Duda, David, and Walker, Alexander
- Subjects
- *
L-functions , *COEFFICIENTS (Statistics) , *NUMBER theory , *COMPLEX numbers , *MATHEMATICAL sequences , *HOLOMORPHIC functions - Abstract
We extend the axiomatization for detecting and quantifying sign changes of Meher and Murty [24] to sequences of complex numbers. We further generalize this result when the sequence is comprised of the coefficients of an L -function. As immediate applications, we prove that there are sign changes in intervals within sequences of coefficients of GL ( 2 ) holomorphic cusp forms, GL ( 2 ) Maass forms, and GL ( 3 ) Maass forms. Building on [13,14] , we prove that there are sign changes in intervals within sequences of partial sums of coefficients of GL ( 2 ) holomorphic cusp forms and Maass forms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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