Improving earlier work of Balasubramanian, Conrey and Heath-Brown , we obtain an asymptotic formula for the mean-square of the Riemann zeta-function times an arbitrary Dirichlet polynomial of length T1/2+Î´ , with Î´ = 0:01515 â¯. As an application we obtain an upper bound of the correct order of magnitude for the third moment of the Riemann zeta-function. We also refine previous work of Deshouillers and Iwaniec , obtaining asymptotic estimates in place of bounds. Using the work ofWatt , we compute the mean-square of the Riemann zeta-function times a Dirichlet polynomial of length going up to T3/4 provided that the Dirichlet polynomial assumes a special shape. Finally, we exhibit a conjectural estimate for trilinear sums of Kloosterman fractions which implies the LindelÃ¶f Hypothesis.
|Titolo:||The mean square of the product of the Riemann zeta-function with Dirichlet polynomials|
|Data di pubblicazione:||2017|
|Appare nelle tipologie:||01.01 - Articolo su rivista|