Wyniki wyszukiwania

1

On the Piatetski-Shapiro-Vinogradov Theorem

100%

Jia C.

Acta Arithmetica

|

1995

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tom 73

|

nr 1

1-28

2

Almost all short intervals containing prime numbers

100%

Jia C.

Acta Arithmetica

|

1996

|

tom 76

|

nr 1

21-84

3

On a conjecture of Yiming Long

75%

Jia C.

Acta Arithmetica

|

2006

|

tom 122

|

nr 1

57-61

4

The mean square of the divisor function

64%

Jia C., Sankaranarayanan A.

Acta Arithmetica

|

2014

|

tom 164

|

nr 2

181-208

EN

Let d(n) be the divisor function. In 1916, S. Ramanujan stated without proof that $∑_{n≤x} d²(n) = xP(log x) + E(x)$, where P(y) is a cubic polynomial in y and $E(x) = O(x^{3/5 + ε})$, with ε being a sufficiently small positive constant. He also stated that, assuming the Riemann Hypothesis (RH), $E(x)=O(x^{1/2 + ε})$. In 1922, B. M. Wilson proved the above result unconditionally. The direct application of the RH would produce $E(x) = O(x^{1/2}(log x)⁵loglog x)$. In 2003, K. Ramachandra and A. Sankaranarayanan proved the above result without any assumption. In this paper, we prove $E(x) = O(x^{1/2}(log x)⁵)$.

5

On the largest prime factor of integers

64%

Jia C., Liu M.-C.

Acta Arithmetica

|

2000

|

tom 95

|

nr 1

17-48

Ograniczanie wyników

5 Acta Arithmetica

5 Jia C.

1 Liu M.-C.

1 Sankaranarayanan A.

1 2014

1 2006

1 2000

1 1996

1 1995

On the Piatetski-Shapiro-Vinogradov Theorem

Almost all short intervals containing prime numbers

On a conjecture of Yiming Long

The mean square of the divisor function

On the largest prime factor of integers