Computation of zeros of $L$-function associated with the cubic theta-function
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 23, Tome 357 (2008), pp. 180-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with $L$-function attached to the Kubota–Patterson cubic theta function. We have developed method for numerical computations of the $L$-function values. We have stated some conjectures on distribution of the $L$-function zeros supported by numeric computation. Bibl. – 12 titles.
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N. V. Proskurin. Computation of zeros of $L$-function associated with the cubic theta-function. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 23, Tome 357 (2008), pp. 180-194. http://geodesic.mathdoc.fr/item/ZNSL_2008_357_a10/

[1] T. Kubota, On automorphic functions and reciprocity law in a number theory, Lect. Math. Kyoto Univ., 2, Kinokuniya Book-Store, Tokyo, 1969 | MR | Zbl

[2] S. J. Patterson, “A cubic analogue of the theta series. I”, J. Reine Angew. Math., 296 (1977), 125–161 | DOI | MR | Zbl

[3] N. V. Proskurin, Cubic metaplectic forms and theta functions, Lect. Notes Math., 1677, Springer-Verlag, Berlin, 1998 | MR | Zbl

[4] N. V. Proskurin, “O ryadakh Dirikhle, assotsiirovannykh s kubicheskoi teta-funktsiei”, Zap. nauchn. semin. POMI, 337, POMI, SPb., 2006, 212–232 | MR | Zbl

[5] N. V. Proskurin, “O nulyakh $L$-funktsii, assotsiirovannoi s kubicheskoi teta-funktsiei”, Zap. nauchn. semin. POMI, 350, POMI, SPb., 2007, 173–186 | MR

[6] R. J. Backlund, “Über die Nullstellen der Riemannschen Zeta-funktion”, Acta Math., 41 (1918), 345–375 | DOI | MR | Zbl

[7] K. Chandrasekkharan, Arifmeticheskie funktsii, Nauka, Fizmatlit, M., 1975 | MR

[8] A. F. Lavrik, “O funktsionalnykh uravneniyakh funktsii Dirikhle”, Izv. AN SSSR. Ser. matem., 31:2 (1967), 431–442 | MR | Zbl

[9] F. W. J. Olver, Introduction to asymptotics and special functions, Academic Press, New York–London, 1974 | MR | Zbl

[10] L. N. G. Filon, “On a quadrature formula for trigonometric integrals”, Proc. Roy. Soc. Edinburgh, 49 (1928), 38–47

[11] A. F. Lavrik, “Priblizhënnye funktsionalnye uravneniya funktsii Dirikhle”, Izv. AN SSSR. Ser. matem., 32:1 (1968), 134–185 | MR | Zbl

[12] A. Strömbergsson, Studies in the analitic and spectral theory of automorphic forms, Uppsala dissertations in math. 17, Uppsala Univ., 2001 | MR | Zbl