For twist-inequivalent non-CM newforms, differences, products, and ratios of prime-power Fourier coefficients satisfy each prescribed inequality on a positive-density set of primes, with explicit density bounds.
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An effective equidistribution theorem for pairs of newform Fourier coefficients is extended from rectangles to arbitrary measurable sets with finite-length boundary, with applications to sign changes of symmetric-power coefficients.
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Determining newforms via arithmetic relations among Fourier coefficients
For twist-inequivalent non-CM newforms, differences, products, and ratios of prime-power Fourier coefficients satisfy each prescribed inequality on a positive-density set of primes, with explicit density bounds.
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Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients
An effective equidistribution theorem for pairs of newform Fourier coefficients is extended from rectangles to arbitrary measurable sets with finite-length boundary, with applications to sign changes of symmetric-power coefficients.