H. Iwaniec

Publications245
h-index48
Citations10,756
Highly Influential Citations1,059
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Analytic Number Theory
Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large…
Topics in classical automorphic forms
Introduction The classical modular forms Automorphic forms in general The Eisenstein and the Poincare series Kloosterman sums Bounds for the Fourier coefficients of cusp forms Hecke operators…
Spectral methods of automorphic forms
Introduction Harmonic analysis on the Euclidean plane Harmonic analysis on the hyperbolic plane Fuchsian groups Automorphic forms The spectral theorem. Discrete part The automorphic Green function…
Primes in arithmetic progressions to large moduli
Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Low lying zeros of families of L-functions
In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at…
The cubic moment of central values of automorphic L-functions
The authors study the central values of L-functions in certain families; in particular they bound the sum of the cubes of these values.Contents:
Kloosterman sums and Fourier coefficients of cusp forms
The polynomial $X^2+Y^4$ captures its primes
This article proves that there are infinitely many primes of the form a^2 + b^4, in fact getting the asymptotic formula. The main result is that \sum_{a^2 + b^4\le x} \Lambda(a^2 + b^4) =…
A new form of the error term in the linear sieve
Exponential sums with monomials
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