Large sieve with square moduli for Z[i].

Abstract: The large sieve inequality is of fundamental importance in analytic number theory. Its theory started with Linnik’s investigation of the least quadratic non-residue modulo primes on average. These days, there is a whole zoo of large sieve inequalities in all kind of contexts (for number fields, function fields, automorphic forms, etc.). The large sieve with restricted sets of moduli $q \in \mathbb{Z}$, in particular with square moduli, were investigated by L. Zhao and S. Baier. Moreover, the large sieve with square moduli has found many applications, in particular, in questions regarding elliptic curves. The large sieve for additive characters was extended to number fields by Huxley. In my talk, I will give a summary of the classical large sieve with square moduli and present new extenstions to number field $\mathbb{Q}[i]$ which have recently been established in joint work with Stephan Baier.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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