论文信息 - Averages of exponential twists of the Liouville function

Averages of exponential twists of the Liouville function

Let lOnU denote the Liouville function and consider the sum SOx; aUa P nUx lOnUe 2pina . We prove that for all a of irrational type 1 (that includes all algebraic irra- tionalities) SOx; aUaOOx 4=5ae U for any e > 0. The method is extended to study more general sums of the form P nUx aOnUe 2pina for a general class of arithmetical functions aOnU. The main technique is the Vinogradov-Vaughan method of studying exponential sums. 2000 Mathematics Subject Classification: 11L07; 11N36.

A. Sankaranarayanan | M. Ram Murty

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