On the first occurrence of values of a character

Kolesnik, G.; Straus, E. G.

doi:10.1090/S0002-9947-1978-0515545-6

On the first occurrence of values of a character
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by G. Kolesnik and E. G. Straus PDF

Trans. Amer. Math. Soc. 246 (1978), 385-394 Request permission

Abstract:

Let $\chi$ be a character of order $k (\bmod n)$, and let ${g_m}(\chi )$ be the smallest positive integer at which $\chi$ attains its $(m + 1)$st nonzero value. We consider fixed k and large n and combine elementary group-theoretic considerations with the known results on character sums and sets of integers without large prime factors to obtain estimates for ${g_m}(\chi )$.

References

D. A. Burgess, On character sums and $L$-series. II, Proc. London Math. Soc. (3) 13 (1963), 524–536. MR 148626, DOI 10.1112/plms/s3-13.1.524
James H. Jordan, The distribution of cubic and quintic non-residues, Pacific J. Math. 16 (1966), 77–85. MR 186619, DOI 10.2140/pjm.1966.16.77
Karl K. Norton, Numbers with small prime factors, and the least $k$th power non-residue, Memoirs of the American Mathematical Society, No. 106, American Mathematical Society, Providence, R.I., 1971. MR 0286739
Karl K. Norton, Upper bounds for $k\textrm {th}$ power coset representatives modulo $n$, Acta Arith. 15 (1968/69), 161–179. MR 240065, DOI 10.4064/aa-15-2-161-179

On the bound of the least non-residue of nth powers

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