Abstract
The scalar product of Hecke series with Größencharakteren, introduced by Yu. V. Linnik, and its generalizations are studied. Analytic properties of the functions under consideration are closely related to the distribution of integer points on toric varieties. Bibliography: 22 titles.
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References
Yu. V. Linnik, “A private communication,” March (1962).
B. Z. Moroz, “Analytic continuation of the scalar product of Hecke series of two quadratic fields and its application,” Dokl. Akad. Nauk SSSR, Ser. Mat., 150, 752–754 (1963).
B. Z. Moroz, “On the continuation of the scalar product of Hecke series of two quadratic fields,” Dokl. Akad. Nauk SSSR, Ser. Mat., 155, 1265–1267 (1964).
O. M. Fomenko, “Continuation to the whole plane and a functional equation of the scalar product of Hecke series of two quadratic series,” Trudy MIAN SSSR, 128, 232–241 (1972).
A. I. Vinogradov, “On the continuation to the left half-plane of the scalar product of the Hecke L-series,” Izv. AB SSSR, 29, 485–492 (1965).
P. K. J. Draxl, “L-Funktionen algebraischer Tori,” J. Number Theory, 3, 444–467 (1971).
N. Kurokawa, “On the meromorphy of Euler products,” Proc. Jpn. Acad., 54A, 163–166 (1978).
N. Kurokawa, “On Linnik’s problem,” Proc. Jpn. Acad., 54A, 167–169 (1978).
N. Kurokawa, “On the meromorphy of Euler products. I, II,” Proc. London Math. Soc., 53, 1–47, 209–236 (1986).
B. Z. Moroz, “On the distribution of integral points on an algebraic torus defined by a system of norm-form equations,” Quart. J. Math. (2), 45, 243–253 (1994).
B. Z. Moroz, “Exercises in analytic arithmetic on an algebraic torus,” in: Israel Mathematical Conferences Proceedings (F. Hirzebruch Festband), 9 (1996), pp. 347–359.
B. Z. Moroz, “On the integer points of some toric varieties,” Quart. J. Math. (2), 48, 67–82 (1997).
B. Z. Moroz, “On the distribution of integer points in the real locus of an affine toric variety,” Lect. Notes Math., 237, 283–291 (1997).
B. Z. Moroz, “On the integer points of an affine toric variety (general case),” Quart. J. Math. (2), 50, 37–47 (1999).
B. Z. Moroz, “On a class of Dirichlet series associated to the ring of representations of a Weil group,” Proc. London Math. Soc., 56, 209–228 (1988).
J. Tate, “Automorphic forms, representations, and L-functions” [Russian translation], in: Number Theoretic Introduction, Mir, Moscow (1984), pp. 73–112.
A. Weil, “Sur la théorie du corps de classes,” J. Math. Soc. Jpn., 3, 1–35 (1951).
B. Z. Moroz, “Equidistribution of Frobenius classes and the volumes of tubes,” Acta Arith., 51, 269–276 (1988).
B. Z. Moroz, “Scalar product of Hecke L-functions and its application,” Adv. Stud. Pure Math., 21, 153–171 (1992).
B. Z. Moroz, “Analytic arithmetic in algebraic number fields,” Lect. Notes Math., 1205 (1986).
B. E. Kunyavskii and B. Z. Moroz, “On integral models of affine toric varieties,” Trudy St.Petersburg Mat. Obshch., 7, 116–123 (1999).
B. E. Kunyavskii and B. Z. Moroz, “On integral models of algebraic tori and of affine toric varieties,” to appear.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 135–148.
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Moroz, B.Z. Scalar products of dirichlet series and the distribution of integer points on toric varieties. J Math Sci 137, 4690–4698 (2006). https://doi.org/10.1007/s10958-006-0265-9
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DOI: https://doi.org/10.1007/s10958-006-0265-9