AN EXTENSION OF THE BOURGAIN–SARNAK–ZIEGLER THEOREM WITH MODULAR APPLICATIONS

Author:

Cafferata M1,Perelli A2,Zaccagnini A1

Affiliation:

1. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy

2. Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy

Abstract

Abstract We first prove an extension of the Bourgain–Sarnak–Ziegler theorem, relaxing some conditions and giving quantitative estimates. Then we apply our extension to bound certain exponential sums, where the coefficients come from modular forms and the exponential involves polynomial sequences of any degree.

Funder

MIUR

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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