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Bounds for the coefficients of powers of the Δ‐function
Author(s) -
Rouse Jeremy
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn094
Subject(s) - mathematics , constant (computer programming) , zero (linguistics) , value (mathematics) , function (biology) , combinatorics , statistics , philosophy , linguistics , evolutionary biology , computer science , biology , programming language
For k ⩾1, let∑ n = k ∞ τ k ( n ) q n = q k Π n = 1 ∞( 1 − q n ) 24 k. It follows from Deligne's proof of the Weil conjectures that there is a constant C k so that | τ k ( n )|⩽ C k d ( n ) n (12 k −1)/2 . We study the value of C k as a function of k , and show that it tends to zero very rapidly.