A Bombieri-type theorem for exponential sums (Q381074)
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scientific article; zbMATH DE number 6227346
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Bombieri-type theorem for exponential sums |
scientific article; zbMATH DE number 6227346 |
Statements
A Bombieri-type theorem for exponential sums (English)
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15 November 2013
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Let \(\Omega(n)\) be the number of prime divisors of \(n>1\), and let \(f_k(n)\) denote the characteristic function of \(n\) with \(\Omega(n)=k\). This paper establishes a Bombieri-type mean value theorem for the exponential sum \[ T_k(x,\alpha)=\sum_{n\leq x}f_k(n)e(n\alpha), \] by using the modified Huxley-Hooley contour and the large-sieve type zero-density estimate for Dirichlet \(L\)-functions.
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zero-density estimate
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Huxley-Hooley contour
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Bombieri-type theorem
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