In finite Galois extensions of with pairwise coprime discriminants the integral and the prime divisors subject to the condition are equidistributed in the sense of E. Hecke.
Dans des extensions finies galoisiennes de de discriminants premiers entre eux deux à deux, les diviseurs entiers et les diviseurs premiers soumis à la condition sont équidistribués dans le sens de E. Hecke.
@article{AIF_1984__34_4_1_0, author = {Moroz, Baruch Z.}, title = {On the distribution of integral and prime divisors with equal norms}, journal = {Annales de l'Institut Fourier}, pages = {1--17}, publisher = {Imprimerie Durand}, address = {Chartres}, volume = {34}, number = {4}, year = {1984}, doi = {10.5802/aif.986}, mrnumber = {86c:11075}, zbl = {0525.12013}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.986/} }
TY - JOUR AU - Moroz, Baruch Z. TI - On the distribution of integral and prime divisors with equal norms JO - Annales de l'Institut Fourier PY - 1984 SP - 1 EP - 17 VL - 34 IS - 4 PB - Imprimerie Durand PP - Chartres UR - http://www.numdam.org/articles/10.5802/aif.986/ DO - 10.5802/aif.986 LA - en ID - AIF_1984__34_4_1_0 ER -
%0 Journal Article %A Moroz, Baruch Z. %T On the distribution of integral and prime divisors with equal norms %J Annales de l'Institut Fourier %D 1984 %P 1-17 %V 34 %N 4 %I Imprimerie Durand %C Chartres %U http://www.numdam.org/articles/10.5802/aif.986/ %R 10.5802/aif.986 %G en %F AIF_1984__34_4_1_0
Moroz, Baruch Z. On the distribution of integral and prime divisors with equal norms. Annales de l'Institut Fourier, Volume 34 (1984) no. 4, pp. 1-17. doi : 10.5802/aif.986. http://www.numdam.org/articles/10.5802/aif.986/
[1] Eine neue Art von Zetafunktionen und ihre Bezeihungen zur Verteilung der Primzahlen, Math. Zeitschrift, 6 (1920), 11-51. | JFM
,[2] Distribution of integral ideals with equal norms in the fields of algebraic numbers, I.H.E.S. Preprint, October 1982.
,[3] Primzahlen reel-quadratischer Zahlkörper in Winkelräumen Math. Annalen, 111 (1935), 209-228. | JFM | Zbl
,[4] One some problems in geometry of numbers, Math. Sbornik USSR, 31 (1952), 507-542.
,[5] Generalized Prime Number Theorem, Japanese Journal of Mathematics, 26 (1956), 1-42. | MR | Zbl
,[6] Zetafunktionen und L-funktionen zu Funktionenkörpern vom Fermatschen Typus, § 9, Gesammelte Werke, Bd. II, p. 487-497. | Zbl
,[7] 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] Ergodic properties of algebraic fields, Springer Verlag, 1968, Chapter IX. | Zbl
,[9] 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] On converse theorems for GL(2) and GL(1), American Journal of Mathematics, 103 (1981), 883. | MR | Zbl
,[11] Private communications.
,[12] On Linnik's Problem, Proc. Japan Academy, 54 A (1978), 167-169 (see also: Tokyo Institute of Technology Preprint, 1977). | MR | Zbl
,[13] Scalar products of L-functions with Grössencharacters, J. für die reine und angewandte Mathematik, Bd. 332 (1982), 99-117. | MR | Zbl
,[14] On the convolution of L-functions, Mathematika, 27 (1980), 312-320. | MR | Zbl
,[15] Theory of Riemann Zeta-function, Oxford, 1951. | MR | Zbl
,[16] On the zeros of Hecke's L-functions I, Acta Arithmetica, 7 (1961/1962), 87-106. | MR | Zbl
,[17] On ideal classes of number fields containing integral ideals of equal norms, Journal of Number Theory, to appear. | Zbl
, ,[18] Über die Gleichverteilung von Zahlen mod Eins. Math. Annalen, 77 (1916), 313-352. | JFM
,[19] L-funktionen Algebraischer Tori, Journal of Number Theory, 3 (1971), 444-467. | MR | Zbl
,[20] 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] Functions L et représentation simultanée d'un nombre premier par plusieurs formes quadratiques, Séminaire Delange-Pisot-Poitou, 12e année, 1970/1971. | Numdam | Zbl
,[22] The approximate functional equation for a class of zeta-functions, Math. Ann., 152 (1963), 30-64. | MR | Zbl
, ,[23] On the number of Integral Ideals in Galois Extensions, Monatshefte für Mathematik, 95 (1983), 99-109. | MR | Zbl
, ,[24] Sums of powers of cusp form coefficients, Math. Ann., 263 (1983), 227-236. | MR | Zbl
,Cited by Sources: