Showing papers by "Henryk Iwaniec published in 2007"
TL;DR: In this paper, the first sign change of the Hecke eigenvalues of a normalized cuspidal newform of level N has been studied and a new estimate was given.
Abstract: We shall improve earlier estimates on the first sign change of the Hecke eigenvalues of a normalized cuspidal newform of level N.
51 citations
TL;DR: In this article, the orthogonalities of Hecke eigenvalues of holomorphic cusp forms were studied and an asymptotic large sieve with an unusually large main term was obtained.
Abstract: In this paper, we study the orthogonalities of Hecke eigenvalues of holomorphic cusp forms. An asymptotic large sieve with an unusually large main term for cusp forms is obtained. A family of special vectors formed by products of Kloosterman sums and Bessel functions is constructed for which the main term is exceptionally large. This surprising phenomenon reveals an interesting fact: that Fourier coefficients of cusp forms favor the direction of products of Kloosterman sums and Bessel functions of compatible type.
26 citations
Posted Content•
TL;DR: In this article, it was shown that the constant 42 appears as a factor in the leading order term of the Riemann zeta function, exactly as is predicted for the 6th moment of Dirichlet L-functions.
Abstract: We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $\chi$ modulo $q$, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.
22 citations
01 Jan 2007
TL;DR: In this article, an optimal level of distribution result sequence of integers of the type X^2+Y^{2r} was given for integers of type X 2 + Y 2 r.
Abstract: We prove an optimal `level of distribution' result sequences of integers of the type $X^2+Y^{2r}$.
9 citations
Posted Content•
26 Oct 2007
TL;DR: In this paper, it was shown that the constant 42 appears as a factor in the leading order term of the Riemann zeta function, exactly as is predicted for the 6th moment of Dirichlet L-functions.
Abstract: We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $\chi$ modulo $q$, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.
2 citations