Wyniki wyszukiwania

1

On representing the multiple of a number by a quadratic form

100%

Cochrane T.

Acta Arithmetica

|

1993

|

tom 63

|

nr 3

211-222

2

Exponential sums modulo prime powers

88%

Cochrane T.

Acta Arithmetica

|

2002

|

tom 101

|

nr 2

131-149

3

Pure and mixed exponential sums

64%

Cochrane T., Zheng Z.

Acta Arithmetica

|

1999

|

tom 91

|

nr 3

249-278

4

Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)

64%

Ayyad A., Cochrane T.

Acta Arithmetica

|

2008

|

tom 132

|

nr 2

127-133

5

Exponential sums with rational function entries

64%

Cochrane T., Zheng Z.

Acta Arithmetica

|

2000

|

tom 95

|

nr 1

67-95

6

A further refinement of Mordell's bound on exponential sums

51%

Cochrane T., Coffelt J., Pinner C.

Acta Arithmetica

|

2005

|

tom 116

|

nr 1

35-41

7

Waring's number for large subgroups of ℤₚ

51%

Cochrane T., Hart D., Pinner C., Spencer C.

Acta Arithmetica

|

2014

|

tom 163

|

nr 4

309-325

EN

Let p be a prime, ℤₚ be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero kth powers in ℤₚ. The goal of this paper is to determine, for a given positive integer s, a value tₛ such that if |A| ≫ tₛ then every element of ℤₚ is a sum of s kth powers. We obtain $t₄ = p^{22/39+ϵ}$, $t₅ = p^{15/29+ϵ}$ and for s ≥ 6, $tₛ = p^{(9s+45)/(29s+33)+ϵ}$. For s ≥ 24 further improvements are made, such as $t_{32} = p^{5/16+ϵ}$ and $t_{128} = p^{1/4}$.

8

On the parity of k-th powers modulo p. A generalization of a problem of Lehmer

51%

Bourgain J., Cochrane T., Paulhus J., Pinner C.

Acta Arithmetica

|

2011

|

tom 147

|

nr 2

173-203

9

Sparse polynomial exponential sums

51%

Cochrane T., Pinner C., Rosenhouse J.

Acta Arithmetica

|

2003

|

tom 108

|

nr 1

37-52

10

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Strong Riesz sets and polynomials

45%

Cochrane T., Dressler R. E.

Colloquium Mathematicum

|

1989-1990

|

tom 58

|

nr 1

23-27

Ograniczanie wyników

9 Acta Arithmetica

1 Colloquium Mathematicum

10 Cochrane T.

4 Pinner C.

2 Zheng Z.

1 Ayyad A.

1 Bourgain J.

1 Coffelt J.

1 Dressler R. E.

1 Hart D.

1 Paulhus J.

1 Rosenhouse J.

1 Spencer C.

1 2014

1 2011

1 2008

1 2005

1 2003

1 2002

1 2000

1 1999

1 1993

1 1989

On representing the multiple of a number by a quadratic form

Exponential sums modulo prime powers

Pure and mixed exponential sums

Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)

Exponential sums with rational function entries

A further refinement of Mordell's bound on exponential sums

Waring's number for large subgroups of ℤₚ

On the parity of k-th powers modulo p. A generalization of a problem of Lehmer

Sparse polynomial exponential sums

Strong Riesz sets and polynomials

Ograniczanie wyników

Wyniki wyszukiwania

On representing the multiple of a number by a quadratic form

Exponential sums modulo prime powers

Pure and mixed exponential sums

Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)

Exponential sums with rational function entries

A further refinement of Mordell's bound on exponential sums

Waring's number for large subgroups of ℤ*ₚ*

On the parity of k-th powers modulo p. A generalization of a problem of Lehmer

Sparse polynomial exponential sums

Strong Riesz sets and polynomials

Waring's number for large subgroups of ℤₚ