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JOURNALS // Algebra i Analiz

Algebra i Analiz, 2005, Volume 17, Issue 6, Pages 184–206 (Mi aa718)

On the value distribution for $L(1,\mathrm{sym}^2f)$
O. M. Fomenko

References

1. Hoffstein J., Lockhart P., “Coefficients of Maass forms and the Siegel zero (with an appendix by D. Goldfeld, J. Hoffstein, and D. Lieman, An effective zero free region)”, Ann. of Math. (2), 140 (1994), 161–181  crossref  mathscinet  zmath
2. Chowla S., Erdös P., “A theorem on the distribution of values of $L$-functions”, J. Indian Math. Soc. (N.S.), 15 (1951), 11–18  mathscinet  zmath
3. Barban M. B., ““Bolshoe resheto” Yu. V. Linnika i predelnaya teorema dlya chisla klassov idealov mnimogo kvadratichnogo polya”, Izv. AN SSSR. Ser. mat., 26:4 (1962), 573–580  mathnet  mathscinet  zmath
4. Barban M. B., “Metod “bolshogo resheta” i ego primeneniya v teorii chisel”, Uspekhi mat. nauk, 21:1(127) (1966), 51–102  mathnet  mathscinet  zmath
5. Fainleib A. S, “O predelnoi teoreme dlya chisla klassov chisto korennykh kvadratichnykh form otritsatelnogo opredelitelya”, Dokl. AN SSSR, 184:5 (1969), 1048–1049  mathnet  mathscinet  zmath
6. Fainleib A. S., “O raspredelenii chisla klassov polozhitelnykh kvadratichnykh form”, Nauch. tr. Tashkent. un-ta, 418, Tashkent, 1972, 272–279  mathscinet  zmath
7. Elliott P. D. T. A., “The distribution of the quadratic class number”, Lit. mat. sb., 10:1 (1970), 189–197  mathscinet  zmath
8. Luo W., “Values of symmetric square $L$-functions at 1”, J. Reine Angew. Math., 506 (1999), 215–235  mathscinet  zmath
9. Royer E., “Statistique de la variable aléatoire $L(\text{sym}^2f,1)$”, Math. Ann., 321:3 (2001), 667–687  crossref  mathscinet  zmath
10. Fomenko O. M., “Povedenie avtomorfnykh $L$-funktsii v tochkakh $s=1$ i $s=\frac12$”, Zap. nauch. semin. POMI, 302, 2003, 149–167  mathnet
11. Fomenko O. M., “Avtomorfnye $L$-funktsii v aspekte po vesu”, Zap. nauch. semin. POMI, 314, 2004, 221–246  mathnet  zmath
12. Fomenko O. M., “O raspredelenii znachenii $L(1,f)$”, Zap. nauch. semin. POMI, 302, 2003, 135–148  mathnet
13. Golubeva E. P., “Raspredelenie znachenii $L$-funktsii Gekke v tochke 1”, Zap. nauch. semin. POMI, 314, 2004, 15–32  mathnet  zmath
14. Ivić A., The Riemann zeta-function, Wiley, New York etc., 1985  mathscinet  zmath
15. Sarnak P., “Statistical properties of eigenvalues of the Hecke operators”, Analytic Number Theory and Diophantine Problems (Stillwater, OK, 1984), Progr. Math., 70, Birkhäuser Boston, Boston, MA, 1987, 321–331  mathscinet
16. Serre J.-P., “Répartition asymptotique des valeurs propres de l'opérateur de Hecke $T_p$”, J. Amer. Math. Soc., 10:1 (1997), 75–102  crossref  mathscinet  zmath
17. Conrey J. B., Duke W., Farmer D. W., “The distribution of the eigenvalues of Hecke operators”, Acta Arith., 78:4 (1997), 405–409  mathscinet  zmath
18. Golubeva E. P., “Raspredelenie sobstvennykh chisel operatorov Gekke”, Zap. nauch. semin. POMI, 314, 2004, 33–40  mathnet  mathscinet  zmath
19. Montgomeri G., Multiplikativnaya teoriya chisel, Mir, M., 1974  mathscinet
20. Mardzhanishvili K. K., “Otsenka odnoi arifmeticheskoi summy”, Dokl. AN SSSR, 22:7 (1939), 391–393
21. Fainleib A. S., “Obobschenie neravenstva Esseena i ego primenenie v veroyatnostnoi teorii chisel”, Izv. AN SSSR. Ser. mat., 32:4 (1968), 859–879  mathnet  mathscinet  zmath


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