Math @ Duke

Publications [#302477] of Caroline TurnageButterbaugh
Papers Published
 Barrett, O; McDonald, B; Miller, SJ; Ryan, P; TurnageButterbaugh, CL; Winsor, K, Gaps between zeros of GL(2) Lfunctions,
Journal of Mathematical Analysis and Applications, vol. 429 no. 1
(September, 2015),
pp. 204232, ISSN 0022247X [arXiv:1410.7765], [doi]
(last updated on 2018/02/22)
Abstract: © 2015 Elsevier Inc.Let L(s, f) be an Lfunction associated to a primitive (holomorphic or Maass) cusp form f on GL(2) over Q. Combining meanvalue estimates of Montgomery and Vaughan with a method of Ramachandra, we prove a formula for the mixed second moments of derivatives of L(1/2 + it, f) and, via a method of Hall, use it to show that there are infinitely many gaps between consecutive zeros of L(s, f) along the critical line that are at least √3=1.732. . . times the average spacing. Using general pair correlation results due to Murty and Perelli in conjunction with a technique of Montgomery, we also prove the existence of small gaps between zeros of any primitive Lfunction of the Selberg class. In particular, when f is a primitive holomorphic cusp form on GL(2) over Q, we prove that there are infinitely many gaps between consecutive zeros of L(s, f) along the critical line that are at most 0.823 times the average spacing.


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