Abstract
We consider the simultaneous sign changes of normalized Fourier coefficients associated to two distinct Hecke eigenforms supported at positive integers represented by a primitive integral binary quadratic form with negative discriminant whose class number is 1. We provide a quantitative result for the number of sign changes of such sequence in the interval \((x,2x]\) for sufficiently large \(x\).
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Acknowledgements
The author would like to express his gratitude to Professor Guangshi Lü and Professor Bin Chen for their constant encouragement and valuable suggestions. The author is extremely grateful to the anonymous referee for meticulous checking, for thoroughly reporting countless typos and inaccuracies as well as for valuable comments. These corrections and additions have made the manuscript clearer and readable.
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This work is supported in part by the National Key Research and Development Program of China (Grant No. 2021YFA1000700).
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HUA, G. ON THE SIMULTANEOUS SIGN CHANGES OF HECKE EIGENVALUES OVER AN INTEGRAL BINARY QUADRATIC FORM. Acta Math. Hungar. 167, 476–491 (2022). https://doi.org/10.1007/s10474-022-01252-z
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DOI: https://doi.org/10.1007/s10474-022-01252-z