no. 4
On the distribution of integral and prime divisors with equal norms
Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 1-17.

Dans des extensions finies galoisiennes k 1 ,...,k r de Q de discriminants premiers entre eux deux à deux, les diviseurs entiers et les diviseurs premiers soumis à la condition N k 1 /Q 𝔞 r =⋯=N k r /Q 𝔞 r sont équidistribués dans le sens de E. Hecke.

In finite Galois extensions k 1 ,...,k r of Q with pairwise coprime discriminants the integral and the prime divisors subject to the condition N k 1 /Q 𝔞 r =⋯=N k r /Q 𝔞 r are equidistributed in the sense of E. Hecke.

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Moroz, Baruch Z. On the distribution of integral and prime divisors with equal norms. Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 1-17. doi : 10.5802/aif.986. https://aif.centre-mersenne.org/articles/10.5802/aif.986/

[1] E. Hecke, Eine neue Art von Zetafunktionen und ihre Bezeihungen zur Verteilung der Primzahlen, Math. Zeitschrift, 6 (1920), 11-51. | JFM

[2] B. Z. Moroz, Distribution of integral ideals with equal norms in the fields of algebraic numbers, I.H.E.S. Preprint, October 1982.

[3] H. Rademacher, Primzahlen reel-quadratischer Zahlkörper in Winkelräumen Math. Annalen, 111 (1935), 209-228. | JFM | Zbl

[4] J. P. Kubilius, One some problems in geometry of numbers, Math. Sbornik USSR, 31 (1952), 507-542.

[5] T. Mitsui, Generalized Prime Number Theorem, Japanese Journal of Mathematics, 26 (1956), 1-42. | MR | Zbl

[6] H. Hasse, Zetafunktionen und L-funktionen zu Funktionenkörpern vom Fermatschen Typus, § 9, Gesammelte Werke, Bd. II, p. 487-497. | Zbl

[7] T. Mitsui, Some prime number theorems for algebraic number fields, Proc. Sympos. Res. Inst. Math. Sci., Kyoto Univ., Kyoto 1977, N. 294, p. 100-123 (MR 57 # 3092). | MR | Zbl

[8] Yu. V. Linnik, Ergodic properties of algebraic fields, Springer Verlag, 1968, Chapter IX. | Zbl

[9] E. P. Golubeva, On representation of large numbers by ternary quadratic forms, Doklady Acad. of Sci. of the U.S.S.R., 191 (1970), 519-521. | MR | Zbl

[10] W.-Ch. W. Li, On converse theorems for GL(2) and GL(1), American Journal of Mathematics, 103 (1981), 883. | MR | Zbl

[11] Yu. V. Linnik, Private communications.

[12] N. Kurokawa, On Linnik's Problem, Proc. Japan Academy, 54 A (1978), 167-169 (see also: Tokyo Institute of Technology Preprint, 1977). | MR | Zbl

[13] B. Z. Moroz, Scalar products of L-functions with Grössencharacters, J. für die reine und angewandte Mathematik, Bd. 332 (1982), 99-117. | MR | Zbl

[14] B. Z. Moroz, On the convolution of L-functions, Mathematika, 27 (1980), 312-320. | MR | Zbl

[15] E. C. Titchmarsh, Theory of Riemann Zeta-function, Oxford, 1951. | MR | Zbl

[16] H. Fogels, On the zeros of Hecke's L-functions I, Acta Arithmetica, 7 (1961/1962), 87-106. | MR | Zbl

[17] W.-Ch. W. Li, B. Z. Moroz, On ideal classes of number fields containing integral ideals of equal norms, Journal of Number Theory, to appear. | Zbl

[18] H. Weyl, Über die Gleichverteilung von Zahlen mod Eins. Math. Annalen, 77 (1916), 313-352. | JFM

[19] P.K.J. Draxl, L-funktionen Algebraischer Tori, Journal of Number Theory, 3 (1971), 444-467. | MR | Zbl

[20] A. I. Vinogradov On the extension to the left half-plane of the scalar product of Hecke's L-series with Grössencharacters, Izvestia U.S.S.R. Acad. of Sci., Math. Series, 29 (1965), 485-492.

[21] P. K. J. Draxl, Functions L et représentation simultanée d'un nombre premier par plusieurs formes quadratiques, Séminaire Delange-Pisot-Poitou, 12e année, 1970/1971. | Numdam | Zbl

[22] K. Chandrasekharan, R. Narasimhan, The approximate functional equation for a class of zeta-functions, Math. Ann., 152 (1963), 30-64. | MR | Zbl

[23] K. Chandrasekharan, A. Good, On the number of Integral Ideals in Galois Extensions, Monatshefte für Mathematik, 95 (1983), 99-109. | MR | Zbl

[24] R. A. Rankin, Sums of powers of cusp form coefficients, Math. Ann., 263 (1983), 227-236. | MR | Zbl

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