On a Linnik problem for elliptic curves
Copyright policy )On a Linnik problem for elliptic curves
Let S ( Q , B ) S(Q,B) denote the number of moduli q ≤ Q q\leq Q for which a primitive character χ \chi mod q q exists such that n χ > B n_{\chi }>B , where n χ n_{\chi } denotes the smallest natural number such that χ ( n ) ≠ 1 \chi (n) \not =1 . Baier showed that for any β > 2 \beta >2 we have S ( Q , ( log Q ) β ) ≪ Q 1 β − 1 + ε S(Q,(\log Q)^{\beta }) \ll Q^{\frac {1}{\beta -1}+\varepsilon } and asked for an analogue of this result for elliptic curves. It is the aim of this note to establish such an analogue.
- Institute of Mathematics Poland
- Polish Academy of Sciences Poland
- University of Warsaw Poland
- University of Szczecin Poland
symmetric square, Fourier coefficients of automorphic forms, Elliptic curves over global fields, Applications of sieve methods, modular form, large sieve, elliptic curve
symmetric square, Fourier coefficients of automorphic forms, Elliptic curves over global fields, Applications of sieve methods, modular form, large sieve, elliptic curve
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!