An orthogonal test of the L -functions Ratios conjecture
نویسندگان
چکیده
منابع مشابه
An Orthogonal Test of the L-functions Ratios Conjecture, Ii
Recently Conrey, Farmer, and Zirnbauer [CFZ1, CFZ2] developed the Lfunctions Ratios conjecture, which gives a recipe that predicts a wealth of statistics, from moments to spacings between adjacent zeros and values of L-functions. The problem with this method is that several of its steps involve ignoring error terms of size comparable to the main term; amazingly, the errors seem to cancel and th...
متن کاملAn Orthogonal Test of the L-functions Ratios Conjecture
We test the predictions of the L-functions Ratios Conjecture for the family of cuspidal newforms of weight k and level N , with either k fixed and N → ∞ through the primes or N = 1 and k → ∞. We study the main and lower order terms in the 1-level density. We provide evidence for the Ratios Conjecture by computing and confirming its predictions up to a power savings in the family’s cardinality, ...
متن کاملA Symplectic Test of the L-Functions Ratios Conjecture
Recently Conrey, Farmer and Zirnbauer [CFZ1, CFZ2] conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the main and lower order terms for many problems, ranging from n-level correlations and densities to mollifiers and moments to vanishing at the central point. There are now many results showing agre...
متن کاملApplications of the L-functions Ratios Conjectures
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-f...
متن کاملAutocorrelation of Ratios of L-functions
Conjectures for the moments of L-functions have been sought for many decades, with very little progress until the introduction of random matrix theory into the subject [3, 26, 27]. The predictions using random matrix theory provide plausible conjectures for the leading order asymptotics of the moments of a family of L-functions. More recently, conjectures for all of the main terms of the moment...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2009
ISSN: 0024-6115
DOI: 10.1112/plms/pdp009