Суммы И Произведения Множеств И Оценки Рациональных Тригонометрических Сумм В Полях Простого Порядка

We study exponential sums of the form N n=1 e 2πiab n /m for non-zero integers a, b, m. Classically, non-trivial bounds were known for N ≥ √ m by Korobov, and this range has been extended significantly by Bourgain as a result of his and others' work on the sum-product phenomenon. We use a new technique, similar to the Weyl-van der Corput method of differencing, to give more explicit bounds bounds that become nontrivial around the time when exp(log m/ log 2 log m) ≤ N . We include applications to the digits of rational numbers and constructions of normal numbers.

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Exponential sums in prime fields for modular forms

Bajpai

Bhakta

Garcia

2022

Res. number theory

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Суммы И Произведения Множеств И Оценки Рациональных Тригонометрических Сумм В Полях Простого Порядка

Cited by 8 publications

References 73 publications

Exponential sum estimates over a subgroup in an arbitrary finite field

Exponential sum estimates over a subgroup in an arbitrary finite field

Differencing methods for Korobov-type exponential sums

Exponential sums in prime fields for modular forms

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