Henryk Iwaniec, Rutgers University, Piscataway, NJ.Emmanuel Kowalski, Universite Bordeaux I, Talence, France.

• IntroductionArithmetic functionsElementary theory of prime numbersCharactersSummation formulasClassical analytic theory of $L$-functionsElementary sieve methodsBilinear forms and the large sieveExponential sumsThe Dirichlet polynomialsZero-density estimatesSums over finite fieldsCharacter sumsSums over primesHolomorphic modular formsSpectral theory of automorphic formsSums of Kloosterman sumsPrimes in arithmetic progressionsThe least prime in an arithmetic progressionThe Goldbach problemThe circle methodEquidistributionImaginary quadratic fieldsEffective bounds for the class numberThe critical zeros of the Riemann zeta functionThe spacing of zeros of the Riemann zeta-functionCentral values of $L$-functionsBibliographyIndex

The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" —Zentralblatt Math

Henryk Iwaniec, Rutgers University, Piscataway, NJ.Emmanuel Kowalski, Universite Bordeaux I, Talence, France.

• IntroductionArithmetic functionsElementary theory of prime numbersCharactersSummation formulasClassical analytic theory of $L$-functionsElementary sieve methodsBilinear forms and the large sieveExponential sumsThe Dirichlet polynomialsZero-density estimatesSums over finite fieldsCharacter sumsSums over primesHolomorphic modular formsSpectral theory of automorphic formsSums of Kloosterman sumsPrimes in arithmetic progressionsThe least prime in an arithmetic progressionThe Goldbach problemThe circle methodEquidistributionImaginary quadratic fieldsEffective bounds for the class numberThe critical zeros of the Riemann zeta functionThe spacing of zeros of the Riemann zeta-functionCentral values of $L$-functionsBibliographyIndex

The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" —Zentralblatt Math

Henryk Iwaniec, Rutgers University, Piscataway, NJ.Emmanuel Kowalski, Universite Bordeaux I, Talence, France.

• IntroductionArithmetic functionsElementary theory of prime numbersCharactersSummation formulasClassical analytic theory of $L$-functionsElementary sieve methodsBilinear forms and the large sieveExponential sumsThe Dirichlet polynomialsZero-density estimatesSums over finite fieldsCharacter sumsSums over primesHolomorphic modular formsSpectral theory of automorphic formsSums of Kloosterman sumsPrimes in arithmetic progressionsThe least prime in an arithmetic progressionThe Goldbach problemThe circle methodEquidistributionImaginary quadratic fieldsEffective bounds for the class numberThe critical zeros of the Riemann zeta functionThe spacing of zeros of the Riemann zeta-functionCentral values of $L$-functionsBibliographyIndex

The book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" —Zentralblatt Math