| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Gaps between zeros of GL(2) $L$-functions | Owen Barrett
; Brian McDonald
; Steven J. Miller
; Patrick Ryan
; Caroline L. Turnage-Butterbaugh
; Karl Winsor
; | Date: |
28 Oct 2014 | Abstract: | Let $L(s,f)$ be an $L$-function associated to a primitive (holomorphic or
Maass) cusp form $f$ on GL(2) over $mathbb{Q}$. Combining mean-value 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 $sqrt 3 =
1.732...$ 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 $L$-function
of the Selberg class. In particular, when $f$ is a primitive holomorphic cusp
form on GL(2) over $mathbb{Q}$, 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. | Source: | arXiv, 1410.7765 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |