Applications of the L-functions ratios conjecture

JB Conrey, NC Snaith

Research output: Contribution to journalArticle (Academic Journal)peer-review

66 Citations (Scopus)


In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios 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 functions. In particular, using the ratios conjectures we easily derive the answers to a number of notoriously difficult computations.
Translated title of the contributionApplications of the L-functions ratios conjecture
Original languageEnglish
Pages (from-to)594 - 646
Number of pages53
JournalProceedings of the London Mathematical Society
Volume94 (3)
Publication statusPublished - May 2007

Bibliographical note

Publisher: Oxford University Press

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