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… Expand

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… Expand

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… Expand

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… Expand

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) =… Expand