The Brun-Titchmarsh Theorem on average

An analogue of the Titchmarsh theorem for the Fourier transform on the group of p-adic numbers

P-Adic Numbers Ultrametric Analysis and Applications ◽

10.1134/s2070046617020066 ◽

2017 ◽

Vol 9 (2) ◽

pp. 158-164 ◽

Cited By ~ 3

Author(s):

Sergey S. Platonov

Keyword(s):

Fourier Transform ◽

Titchmarsh Theorem ◽

The Fourier Transform

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The Titchmarsh Theorem

The Bochner Integral ◽

10.1007/978-3-0348-5567-9_15 ◽

1978 ◽

pp. 201-210

Author(s):

Jan Mikusiński

Keyword(s):

Titchmarsh Theorem

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Short Kloosterman Sums for Polynomials over Finite Fields

Canadian Journal of Mathematics ◽

10.4153/cjm-2003-010-0 ◽

2003 ◽

Vol 55 (2) ◽

pp. 225-246 ◽

Cited By ~ 1

Author(s):

William D. Banks ◽

Asma Harcharras ◽

Igor E. Shparlinski

Keyword(s):

Finite Field ◽

Finite Fields ◽

Small Degree ◽

Kloosterman Sums ◽

Degree Relative ◽

Irreducible Polynomials ◽

Arbitrary Polynomial ◽

Polynomials Over Finite Fields ◽

Titchmarsh Theorem

AbstractWe extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.

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