## 40 Citations

### More precise Pair Correlation Conjecture

- Mathematics
- 2002

In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.

### The Tail of the Singular Series for the Prime Pair and Goldbach Problems

- Mathematics
- 2014

We obtain an asymptotic formula for a weighted sum of the square of the tail of the singular series for the Goldbach and prime-pair problems.

### Pair correlation and distribution of prime numbers.

- Mathematics
- 2002

Pair correlation and distribution of prime numbers

### Higher correlations of divisor sums related to primes I: triple correlations

- Mathematics
- 2001

We obtain the triple correlations for a truncated divisor sum related to primes. We also obtain the mixed correlations for this divisor sum when it is summed over the primes, and give some…

### Communications in Mathematical Physics Primes in Short Intervals

- Mathematics
- 2004

Contrary to what would be predicted on the basis of Cramér’s model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x + H) − ψ(x), for 0 ≤ x ≤ N , is…

### Higher moments of primes in short intervals II

- Mathematics
- 2004

Given good knowledge on the even moments, we derive asymptotic formulas for $\lambda$-th moments of primes in short intervals and prove "equivalence" result on odd moments. We also provide numerical…

### More Precise Pair Correlation of Zeros and Primes in Short Intervals

- Mathematics
- 2002

Goldston and Montgomery proved that the strong pair correlation conjecture and two second moments of primes in short intervals are equivalent to each other under the Riemann hypothesis. The paper…

### Harmonic Analysis as found in Analytic Number Theory

- Mathematics, Philosophy
- 2001

A wide variety of questions of Harmonic Analysis arise naturally in various contexts of Analytic Number Theory; in what follows we consider a number of examples of this type.

### Explicit relations between primes in short intervals and exponential sums over primes

- Mathematics
- 2014

Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of…

## References

SHOWING 1-7 OF 7 REFERENCES

### Irregularities in the distribution of primes and twin primes

- Mathematics
- 1975

The maxima and minima of 〈L(x)〉−π(x), 〈R(x)〉−π(x), and 〈L2(x)〉−π2(x) in various intervals up to x = 8×1010 are tabulated. Here π(x) and π2(x) are respectively the number of primes and twin primes not…

### Gaussian unitary ensemble eigenvalues and Riemann zeta function zeros: A nonlinear equation for a new statistic.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

For infinite Gaussian unitary ensemble random matrices the probability density function for the nearest neighbor eignenvalue spacing is computed in terms of the solution of a certain nonlinear equation, which generalizes the \ensuremath{\sigma} form of the Painlev\'e $V$ equation.

### Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes

- Mathematics
- 1923

### On pair orrelations of zeros and primes in short intervals, Analyti Number Theory and Diophantine Problems (Stillwater

- OK, July
- 1984

### The pair orrelation of zeros of the zeta fun tion, Analyti number theory (St

- Louis Univ.,
- 1972

### On the distribution of spa ings between zeros of the zeta fun

- tion, Math. Comp
- 1987

### Tit hmarsh, The Theory of the Riemann Zeta Fun tion, Se ond Edition

- Dept. of Math., Univ. of Mi higan, Ann Arbor, MI 48109{1009,
- 1986