# Normality of numbers generated by the values of polynomials at primes

Yoshinobu Nakai; Iekata Shiokawa

Acta Arithmetica (1997)

- Volume: 81, Issue: 4, page 345-356
- ISSN: 0065-1036

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top## How to cite

topYoshinobu Nakai, and Iekata Shiokawa. "Normality of numbers generated by the values of polynomials at primes." Acta Arithmetica 81.4 (1997): 345-356. <http://eudml.org/doc/207069>.

@article{YoshinobuNakai1997,

author = {Yoshinobu Nakai, Iekata Shiokawa},

journal = {Acta Arithmetica},

keywords = {polynomials at primes; normal numbers; -adic expansion},

language = {eng},

number = {4},

pages = {345-356},

title = {Normality of numbers generated by the values of polynomials at primes},

url = {http://eudml.org/doc/207069},

volume = {81},

year = {1997},

}

TY - JOUR

AU - Yoshinobu Nakai

AU - Iekata Shiokawa

TI - Normality of numbers generated by the values of polynomials at primes

JO - Acta Arithmetica

PY - 1997

VL - 81

IS - 4

SP - 345

EP - 356

LA - eng

KW - polynomials at primes; normal numbers; -adic expansion

UR - http://eudml.org/doc/207069

ER -

## References

top- [1] A. H. Copeland and P. Erdős, Notes on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857-860. Zbl0063.00962
- [2] H. Davenport and P. Erdős, Note on normal decimals, Canad. J. Math. 4 (1952), 58-63. Zbl0046.04902
- [3] L.-K. Hua, Additive Theory of Prime Numbers, Transl. Math. Monograph 13, Amer. Math. Soc., Providence, RI, 1965. Zbl0192.39304
- [4] M. N. Huxley, The Distribution of Prime Numbers, Oxford Math. Monograph, Oxford Univ. Press, 1972. Zbl0248.10030
- [5] Y.-N. Nakai and I. Shiokawa, A class of normal numbers, Japan. J. Math. 16 (1990), 17-29.
- [6] Y.-N. Nakai and I. Shiokawa, A class of normal numbers II, in: Number Theory and Cryptography, J. H. Loxton (ed.), London Math. Soc. Lecture Note Ser. 154, Cambridge Univ. Press, 1990, 204-210.
- [7] Y.-N. Nakai and I. Shiokawa, Discrepancy estimates for a class of normal numbers, Acta Arith. 62 (1992), 271-284.
- [8] J. Schiffer, Discrepancy of normal numbers, ibid. 47 (1986), 175-186.
- [9] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986. Zbl0601.10026
- [10] I. M. Vinogradov, The Method of Trigonometrical, Sums in Number Theory, Nauka, 1971 (in Russian).

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