Characters With Preassigned Values

W. H. Mills

doi:10.4153/CJM-1963-019-3

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k and t be positive integers; let q1, q2, . . . , qt be distinct prime numbers; and let ζ1, ζ2, ... , ζt be kth roots of unity, not necessarily primitive. Recent investigations on consecutive kth power residues have led to the following question: Under what conditions do there exist primes p that have a kth power character X such that

References

1. Artin, E., Galois theory, Notre Dame (1946).Google Scholar

2. Hasse, H., Jber. Deutsch. Math. Verein. Ergänzungsbände, VI (1930).Google Scholar

3. Hilbert, D., Jber. Deutsch. Math. Verein., 4 (1897), 175–546.Google Scholar

4. Kummer, E., Abh. der K. Akad. der Wiss. zu Berlin (1859).Google Scholar

5. Tschebotareff, N., Math. Ann., 95 (1926), 191–228.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Bierstedt, R. G. and Mills, W. H. 1963. On the bound for a pair of consecutive quartic residues of a prime. Proceedings of the American Mathematical Society, Vol. 14, Issue. 4, p. 628.

Jordan, J. H. 1964. Pairs of Consecutive Power Residues or Non-Residues. Canadian Journal of Mathematics, Vol. 16, Issue. , p. 310.

Graham, R. L. 1964. On quadruples of consecutive 𝑘th power residues. Proceedings of the American Mathematical Society, Vol. 15, Issue. 2, p. 196.

Brillhart, John Lehmer, D. H. and Lehmer, Emma 1964. Bounds for pairs of consecutive seventh and higher power residues. Mathematics of Computation, Vol. 18, Issue. 87, p. 397.

Bass, H. 1965. A remark on an arithmetic theorem of Chevalley. Proceedings of the American Mathematical Society, Vol. 16, Issue. 5, p. 875.

Jordan, James H 1969. Consecutive residues or non-residues in the Gaussian integers. Journal of Number Theory, Vol. 1, Issue. 4, p. 477.

Singh, Sahib 1970. Bounds of quadratic residues in arithmetic progression. Journal of Number Theory, Vol. 2, Issue. 2, p. 162.

Rabung, J. R. and Jordan, J. H. 1970. Consecutive power residues or nonresidues. Mathematics of Computation, Vol. 24, Issue. 111, p. 737.

Rabung, John R 1970. Preassigned character values in the Gaussian integers. Journal of Number Theory, Vol. 2, Issue. 3, p. 329.

Lehmer, D. H. Lehmer, Emma and Shanks, Daniel 1970. Integer sequences having prescribed quadratic character. Mathematics of Computation, Vol. 24, Issue. 110, p. 433.

Lakein, Richard B. 1974. Bounds for consecutive kth power residues in the Eisenstein integers. Journal of Number Theory, Vol. 6, Issue. 4, p. 318.

Vegh, Emanuel 1977. kth-Power residue chains. Journal of Number Theory, Vol. 9, Issue. 2, p. 179.

Galovich, Steven and Stein, Sherman 1981. Splittings of Abelian groups by integers. Aequationes Mathematicae, Vol. 22, Issue. 1, p. 249.

Stein, S K. 1987. Splitting groups of prime order. Aequationes Mathematicae, Vol. 33, Issue. 1, p. 62.

Blackburn, Simon and McKee, James 2011. Constructing 𝑘-radius sequences. Mathematics of Computation, Vol. 81, Issue. 280, p. 2439.

Hu, Su and Li, Yan 2011. kth power residue chains of global fields. Glasnik matematicki, Vol. 46, Issue. 1, p. 11.

Yuan, Pingzhi 2022. Nonsingular splittings of cyclic groups. Discrete Mathematics, Vol. 345, Issue. 9, p. 112946.

Article contents

Characters With Preassigned Values

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests