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Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series

100%

Goldston D., Gonek S.

Acta Arithmetica

1998

tom 84

nr 2

155-192

We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications be removed from the final result. Similar results are obtained for the tails of Dirichlet series. Four examples of applications to the Riemann zeta-function are included.

The distribution of inverses modulo a prime in short intervals

81%

Gonek S., Krishnaswami G., Sondhi V.

Acta Arithmetica

2002

tom 102

nr 4

315-322

Ograniczanie wyników

2 Acta Arithmetica

2 Gonek S.

1 Goldston D.

1 Krishnaswami G.

1 Sondhi V.

1 2002

1 1998

Wyniki wyszukiwania

Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series

The distribution of inverses modulo a prime in short intervals