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Finite Fourier Series and Cyclotomy. [PDF]
Proc Natl Acad Sci U S A, 1951 Whiteman AL.
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Doklady Mathematics, 2022
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Russian Academy of Sciences. Izvestiya Mathematics, 1993
In the paper under review the classical Kloosterman sum \[ K(d_ 1, d_ 2;Q) = \sum_{{x_ 1, x_ 2 \text{mod} Q \atop x_ 1x_ 2 \equiv 1 \pmod Q}} \exp \left( 2\pi i {d_ 1x_ 2 + d_ 2 x_ 2 \over Q} \right) \] is expressed in terms of numbers connected with the arithmetic of \(\mathbb{Z}/m \mathbb{Z}\) where ...
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In the paper under review the classical Kloosterman sum \[ K(d_ 1, d_ 2;Q) = \sum_{{x_ 1, x_ 2 \text{mod} Q \atop x_ 1x_ 2 \equiv 1 \pmod Q}} \exp \left( 2\pi i {d_ 1x_ 2 + d_ 2 x_ 2 \over Q} \right) \] is expressed in terms of numbers connected with the arithmetic of \(\mathbb{Z}/m \mathbb{Z}\) where ...
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Journal of Mathematical Sciences, 2005
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2020
These are a set of notes that introduces the classical Kloosterman sums and proves their basic properties. Kloosterman's bound is proved for the sums which is weaker than the sharp Weil bound. Bounds due to Esterman are also proved and also Selberg's identity is proved for Kloosterman sums.
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These are a set of notes that introduces the classical Kloosterman sums and proves their basic properties. Kloosterman's bound is proved for the sums which is weaker than the sharp Weil bound. Bounds due to Esterman are also proved and also Selberg's identity is proved for Kloosterman sums.
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Canadian Mathematical Bulletin, 1973
Let p be an odd prime, n an integer not divisible by p and α a positive integer. For any integer h with (h,pα)=l, is defined as any solution of the congruence (mod,pα). The Kloosterman sum Ap α(n) (see for example [4]) is defined by(1.1)where the dash (') indicates that the letter of summation runs only through a reduced residue system with respect to
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Let p be an odd prime, n an integer not divisible by p and α a positive integer. For any integer h with (h,pα)=l, is defined as any solution of the congruence (mod,pα). The Kloosterman sum Ap α(n) (see for example [4]) is defined by(1.1)where the dash (') indicates that the letter of summation runs only through a reduced residue system with respect to
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