Area, lattice points, and exponential sums M.N. Huxley.

Includes index.

Includes bibliography (p. 484-490) and references

1. The rational line
2. Polygons and area
3. The integer points close to a curve
4. The rational points close to a curve
5. Analytic lemmas
6. Mean value results
7. The simple exponential sum
8. The exponential sum for the lattice point problem
9. Exponential sums with a difference
10. Exponential sums with modular form coefficients
11. The ruled surface method
12. The Hardy-Littlewood method
13. The First Spacing Problem for the double sum
14. The First and Second Conditions
15. Consecutive minor arcs
16. The Third and Fourth Conditions
17. Exponential sum theorems
18. Lattice points and area
19. Further results
20. Sums with modular form coefficients
21. Applications to the Riemann zeta function
22. An application to number theory: prime integer points
23. Related work
24. Further ideas

This volume is concerned with the application of exponential sum techniques to a variety of problems in number theory, in particular the Riemann Zeta Function and the problem of estimating the number of lattice points in regions.