# A paucity problem associated with a shifted integer analogue of the divisor function

@article{Heap2021APP, title={A paucity problem associated with a shifted integer analogue of the divisor function}, author={Winston Heap and Anurag Sahay and Trevor D. Wooley}, journal={Journal of Number Theory}, year={2021} }

## 3 Citations

### Paucity phenomena for polynomial products

- Mathematics
- 2022

. Let P ( x ) ∈ Z [ x ] be a polynomial with at least two distinct complex roots. We prove that the number of solutions ( x 1 , . . . , x k , y 1 , . . . , y k ) ∈ [ N ] 2 k to the equation Y 1 ≤ i ≤…

### Moments of the Hurwitz zeta function on the critical line

- Mathematics
- 2021

. We study the moments M k ( T ; α ) = 2 T T | ζ s, α ) | 2 k dt of the Hurwitz zeta function ζ ( s, α ) on the critical line, s = 1 / 2+ it with a rational shift α ∈ Q . We conjecture, in analogy…

### THE PAUCITY PROBLEM FOR CERTAIN SYMMETRIC DIOPHANTINE EQUATIONS

- MathematicsBulletin of the Australian Mathematical Society
- 2022

<jats:p>Let <jats:inline-formula>
<jats:alternatives>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S000497272200096X_inline1.png" />
…

## References

SHOWING 1-7 OF 7 REFERENCES

### A note on Helson's conjecture on moments of random multiplicative functions

- Mathematics
- 2015

We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towards (dis)proving a…

### Paucity problems and some relatives of Vinogradov's mean value theorem

- Mathematics
- 2021

When k > 4 and 0 6 d 6 (k− 2)/4, we consider the system of Diophantine equations x 1 + . . .+ xjk = y j 1 + . . .+ y k (1 6 j 6 k, j 6= k − d). We show that in this cousin of a Vinogradov system,…

### Moments of random multiplicative functions and truncated characteristic polynomials

- Mathematics
- 2015

We give an asymptotic formula for the $2k$th moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwi\l\l. We also compute the…

### A special case of Vinogradov's mean value theorem

- Mathematics
- 1997

i=1 (xji − y i ) = 0 (1 ≤ j ≤ k) with xi, yi ∈ [1, P ] ∩ Z are of great utility. This is perhaps best illustrated by the seminal works of Vinogradov from the first half of this century (see, for…

### Rational points of bounded height on threefolds

- Mathematics
- 2007

Let ne,f (B) be the number of non-trivial positive integer solutions x0, x1, x2, y0, y1, y2 ≤ B to the simultaneous equations x0 + x e 1 + x e 2 = y e 0 + y e 1 + y e 2, x f 0 + x f 1 + x f 2 = y f 0…

### Radziwi l l, A note on Helson’s conjecture on moments of random multiplicative functions, in Analytic Number

- Theory (Springer,
- 2015