Small zeros of \(L\)-functions of modular forms (Q2759125)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Small zeros of \(L\)-functions of modular forms |
scientific article; zbMATH DE number 1680958
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small zeros of \(L\)-functions of modular forms |
scientific article; zbMATH DE number 1680958 |
Statements
11 December 2001
0 references
modular forms
0 references
\(L\)-functions
0 references
small zeros
0 references
density hypothesis
0 references
distribution
0 references
Small zeros of \(L\)-functions of modular forms (English)
0 references
\textit{N. M. Katz} and \textit{P. Sarnak} [Random matrices, Frobenius eigenvalues, and monodromy, Coll. Publ. 45, Am. Math. Soc., Providence, RI (1999; Zbl 0958.11004)] recently made a ``density conjecture'' concerning the distribution of the zeros of families of \(L\)-functions attached to newforms for the group \(\Gamma _0(N)\), under the assumption of the Riemann hypothesis for these functions. \textit{H. Iwaniec, W. Luo} and \textit{P. Sarnak} [Publ. Math., Inst. Hautes Étud. Sci. 91, 55-131 (2000; Zbl 1012.11041)] verified this conjecture for low lying zeros. The main result in the present paper is that the same conclusion remains valid even if the family of the forms is restricted by an additional condition in terms of values of Atkin-Lehner operators.
0 references
