Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on January 22, 2007
Proceedings of the London Mathematical Society 2007 94(3):594-646; doi:10.1112/plms/pdl021
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
94/3/594    most recent
pdl021v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Conrey, J. B.
Right arrow Articles by Snaith, N. C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

Applications of the L-functions ratios conjectures

J. B. Conrey1,2 and N. C. Snaith3

1 American Institute of Mathematics
360 Portage Ave
Palo Alto, CA 94306
USA
2 School of Mathematics
University of Bristol
Bristol
BS8 1TW
United Kingdom
conrey{at}aimath.org
3 School of Mathematics
University of Bristol
Bristol
BS8 1TW
United Kingdom
N.C.Snaith{at}bris.ac.uk

Received 15 September 2005. Revision received 14 June 2006.

In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L-functions. In this paper we will present various applications of these ratios conjectures to a wide variety of problems that are of interest in number theory, such as lower order terms in the zero statistics of L-functions, mollified moments of L-functions and discrete averages over zeros of the Riemann zeta function. In particular, using the ratios conjectures we easily derive the answers to a number of notoriously difficult computations.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.