Robert, G. Concernant la relation de distribution satisfaite par la fonction \(\phi\) associée à un réseau complexe. (On the distribution relation satisfied by the function \(\phi\) associated to a complex lattice). (French) Zbl 0729.11029 Invent. Math. 100, No. 2, 231-257 (1990). Der Autor setzt das ganze Arsenal klassischer Methoden aus der Theorie elliptischer Funktionen ein, um schöne neue Beispiele für Funktionen mit Distributionsrelation zu konstruieren: Im Kern geht es darum, zu zwei Gittern \(L\subset \Lambda\) vom Index N teilerfremd zu 6 eine Funktion auf dem Torus \({\mathbb{C}}/L\) mit dem Divisor \(N(O)_ L-\sum^{N}_{i=1}(t_ i)_ L\) zu finden, wo die \(t_ i\) ein vollständiges Restsystem von \(\Lambda\) /L durchlaufen. Reviewer: J.Wolfart (Frankfurt / Main) Cited in 3 ReviewsCited in 14 Documents MSC: 11G99 Arithmetic algebraic geometry (Diophantine geometry) 33E05 Elliptic functions and integrals 14H52 Elliptic curves 11H06 Lattices and convex bodies (number-theoretic aspects) 11F03 Modular and automorphic functions 11F20 Dedekind eta function, Dedekind sums Keywords:functions with distribution relation; complex lattice; elliptic functions × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Coates, J., Sinnott, W.: Integrality properties of the values of partial zeta functions. Proc. London Math. Soc.34, 365-384 (1977) · Zbl 0354.12009 · doi:10.1112/plms/s3-34.2.365 [2] Faltings, G.: Calculus on arithmetic surfaces. Ann. Math.119, 387-424 (1984) · Zbl 0559.14005 · doi:10.2307/2007043 [3] Hirzebruch, F., Zagier, D.: The Atiyah-Singer theorem and elementary number theory. (Math. Lectures Series, vol. 3). Berkeley: Publish or Perish 1974 · Zbl 0288.10001 [4] Kubert, D., Lang, S.: Modular units (Grundleh. der math. Wiss., vol. 244). Berlin-Heidelberg-New York: Springer 1981 · Zbl 0492.12002 [5] Oukhaba, H.: Texte en préparation [6] Ramachandra, K.: Some applications of Kronecker’s limit formulas. Ann. Math.80, 104-148 (1964) · Zbl 0142.29804 · doi:10.2307/1970494 [7] Robert, G.: Unités elliptiques. Bull. Soc. Math. France Mém.36 (1973) [8] Robert, G.: Nombres de Hurwitz et unités elliptiques. Ann. Sc. Ec. Norm. Sup., IV. Sér.11, 297-389 (1978) · Zbl 0409.12008 [9] Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication. Invent. Math.89, 527-559 (1987) · Zbl 0628.14018 · doi:10.1007/BF01388984 [10] Schertz, R.: Niedere Potenzen elliptischer Einheiten, Proc. Int. Conf. on Class Numbers and Fundamental Units (Japan, June 1986, Katata) 67-88 · Zbl 0615.12013 [11] de Shalit, E.: Iwasawa theory of elliptic curves with complex multiplication. (Persp. in math., vol. 3). New York: Academic Press 1987 · Zbl 0674.12004 [12] Siegel, C.L.: A simple proof of \(\eta ( - 1/\tau ) = \eta (\tau )\sqrt {\tau /i} \) . (Mathematika, vol. 1, p. 4 1954), cf. (Op. Sc., vol. III no 62, Berlin-Heidelberg-New York: Springer 1966 · Zbl 0056.29504 [13] Siegel, C.L.: Lectures notes on advanced analytic number theory. Tata Inst. of Fund. Research Research (1961) Bombay [14] Stark, H.M.:L-Functions ats=1, IV, First Derivatives ats=0. Adv. Math.35, 197-235 (1980) · Zbl 0475.12018 · doi:10.1016/0001-8708(80)90049-3 [15] Weil, A.: Introduction à l’étude des variétés kählériennes. Paris: Hermann 1957 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.