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Fractional moments of automorphic $ L$-functions


Author: O. M. Fomenko
Translated by: G. V. Kuz′mina and O. M. Fomenko
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 321-335
MSC (2010): Primary 11F03
DOI: https://doi.org/10.1090/S1061-0022-2011-01143-4
Published electronically: February 8, 2011
MathSciNet review: 2668129
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Abstract: Upper and lower bounds for fractional moments of automorphic $ L$- functions are found.


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  • 1. D. R. Heath-Brown, Fractional moments of the Riemann zeta function, J. London Math. Soc. (2) 24 (1981), 65-78. MR 0623671 (82h:10052)
  • 2. M. Jutila, On the value distribution of the zeta function on the critical line, Bull. London Math. Soc. 15 (1983), 513-518. MR 0705532 (84j:10049)
  • 3. R. W. K. Odoni, A problem of Rankin on sums of powers of cusp-form coefficients, J. London Math. Soc. (2) 44 (1991), 203-217. MR 1136435 (93d:11048)
  • 4. S. Gelbart and H. Jacquet, A relation between automorphic representations of $ \mathrm{GL}(2)$ and $ \mathrm{GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), 471-542. MR 0533066 (81e:10025)
  • 5. D. Bump and D. Ginzburg, Symmetric square $ L$-functions on $ \mathrm{GL}(r)$, Ann. of Math. (2) 136 (1992), 137-205. MR 1173928 (93i:11058)
  • 6. E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen, Math. Ann. 143 (1961), 75-102. MR 0131389 (24:A1241)
  • 7. R. M. Gabriel, Some results concerning the integrals of moduli of regular functions along certain curves, J. London Math. Soc. 2 (1927), 112-117.
  • 8. H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. (2) 8 (1974), 73-82. MR 0337775 (49:2544)
  • 9. A. Good, The square mean of Dirichlet series associated with cusp forms, Mathematika 29 (1982), 278-295. MR 0696884 (84f:10036)
  • 10. A. Laurinčikas, On moments of zeta-functions associated to certain cusp forms, Algebra and Number Theory: Modern Problems and Applications (Saratov, 2004), Thesis of Dokl., Saratov, 2004, pp. 136-137. (English) MR 2280027 (2007i:11072)
  • 11. C. J. Moreno, The Hoheisel phenomenon for generalized Dirichlet series, Proc. Amer. Math. Soc. 40 (1973), 47-51. MR 0327682 (48:6024)
  • 12. A. Sankaranarayanan, Fundamental properties of symmetric square $ L$-functions. I, Illinois J. Math. 46 (2002), 23-43. MR 1936073 (2004a:11038)
  • 13. M. Koike, Higher reciprocity law, modular forms of weight $ 1$ and elliptic curves, Nagoya Math. J. 98 (1985), 109-115. MR 0792775 (86j:11044)
  • 14. O. M. Fomenko, Mean values connected with the Dedekind zeta function, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 350 (2007), 187-198; English transl., J. Math. Sci. (N.Y.) 150 (2008), no. 3, 2115-2122. MR 2722976
  • 15. D. R. Heath-Brown, The twelfth power moment of the Riemann zeta-function, Quart. J. Math. Oxford (2) 29 (1978), 443-462. MR 0517737 (80d:10059)
  • 16. M. Jutila, Lectures on a method in the theory of exponential sums, Tata Inst. Fund. Res. Lectures on Math. and Phys., vol. 80, Tata Inst. Fund. Res., Bombay, 1987. MR 0910497 (89g:11069)
  • 17. S. Zamarys, On fractional moments of Dirichlet $ L$-functons. II, Liet. Mat. Rink. 46 (2006), no. 4, 606-621. MR 2320367 (2008d:11093)

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Additional Information

O. M. Fomenko
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, 27 Fontanka, St. Petersburg 191023, Russia
Email: fomenko@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2011-01143-4
Keywords: Symmetric square $L$-function, fractional moment, convexity
Received by editor(s): March 20, 2009
Published electronically: February 8, 2011
Additional Notes: The author was partly supported by RFBR (project no. 08-01-00233)
Article copyright: © Copyright 2011 American Mathematical Society

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