The large sieve with square moduli in function fields

On the large sieve with square moduli

We prove an estimate for the large sieve with square moduli which improves a recent result of L. Zhao. Our method uses an idea of D. Wolke and some results from Fourier analysis. Mathematics Subject Classification (2000): 11N35, 11L07, 11B57

The large sieve with sparse sets of moduli

Extending a method of D. Wolke [7], we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares. In this case we obtain an estimate which improves a recent result by L. Zhao [8]. Mathematics Subject Classification (2000): 11N35, 11L07, 11B57

On the Square-free Sieve

where the main term will depend on the application; in general, the error term will depend only on the polynomial P in question, not on the particular quantity being estimated. We can split the error term further into one term that can be bounded for every given P , and a second term, say, δ(P ), which may be rather hard to estimate, and which is unknown for polynomials P of high enough degree....

Moduli spaces with external fields

We consider the geometric structures on the moduli space of static finite energy solutions to the 2 + 1 dimensional unitary chiral model with the Wess–Zummino–Witten (WZW) term. It is shown that the magnetic field induced by the WZW term vanishes when restricted to the moduli spaces constructed from the Grassmanian embeddings, so that the slowly moving solitons can in some cases be approximated...

Notes on the large sieve