On the modified Li criterion for a certain class of L-functions

Journal of Number Theory - Tập 156 - Trang 340-367 - 2015
Anne-Maria Ernvall-Hytönen1, Almasa Odžak2, Lejla Smajlović2, Medina Sušić2
1Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland
2Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina

Tài liệu tham khảo

Avdispahić, 2003, ϕ-variation and Barner–Weil formula, Math. Balkanica, 17, 267 Avdispahić, 2005, Explicit formula for a fundamental class of functions, Bull. Belg. Math. Soc. Simon Stevin, 12, 569, 10.36045/bbms/1133793345 Avdispahić, 2006, A note on Weil's explicit formula, 312 Bombieri, 1999, Complements to Li's criterion for the Riemann hypothesis, J. Number Theory, 77, 274, 10.1006/jnth.1999.2392 Bucur, 2015, On τ-Li coefficients for Rankin–Selberg L-functions, vol. 2 Coffey, 2005, Toward verification of the Riemann hypothesis: application of the Li criterion, Math. Phys. Anal. Geom., 8, 211, 10.1007/s11040-005-7584-9 Droll, 2012 Freitas, 2006, A Li-type criterion for zero-free half-planes of Riemann's zeta function, J. Lond. Math. Soc., 73, 399, 10.1112/S0024610706022599 Jorgenson, 1993, Basic Analysis of Regularized Products and Series, vol. 1564 Jorgenson, 1994, Explicit Formulas for Regularized Products and Series, vol. 1593 Kaczorowski, 1999, On the structure of the Selberg class, I: 0≤d≤1, Acta Math., 182, 207, 10.1007/BF02392574 Karatsuba, 2005, The argument of the Riemann zeta function, Russian Math. Surveys, 60, 433, 10.1070/RM2005v060n03ABEH000848 Lagarias, 2007, Li's coefficients for automorphic L-functions, Ann. Inst. Fourier, 57, 1689, 10.5802/aif.2311 Li, 1997, The positivity of a sequence of numbers and the Riemann hypothesis, J. Number Theory, 65, 325, 10.1006/jnth.1997.2137 Li, 2004, Explicit formulas for Dirichlet and Hecke L-functions, Illinois J. Math., 48, 491, 10.1215/ijm/1258138394 Maślanka, 2004, Li's criterion for the Riemann hypothesis – numerical approach, Opscula Math., 24, 103 Mazhouda, 2015, On the τ-Li coefficients for automorphic L-functions, Rocky Mountain J. Math. Odlyzko Odžak, 2010, On Li's coefficients for the Rankin–Selberg L-functions, Ramanujan J., 21, 303, 10.1007/s11139-009-9175-z Odžak, 2011, On asymptotic behavior of generalized Li coefficients in the Selberg class, J. Number Theory, 131, 519, 10.1016/j.jnt.2010.08.009 Omar, 2011, On the zeros of Dirichlet L-functions, LMS J. Comput. Math., 14, 140, 10.1112/S1461157010000215 Omar, 2014, On the Li coefficients for the Hecke L-functions, Math. Phys. Anal. Geom., 17, 67, 10.1007/s11040-014-9141-x Selberg, 1992, Old and new conjectures and results about a class of Dirichlet series, 367 Smajlović, 2010, On Li's criterion for the Riemann hypothesis for the Selberg class, J. Number Theory, 130, 828, 10.1016/j.jnt.2009.10.012 Voros, 2006, Sharpening of Li's criterion for the Riemann hypothesis, Math. Phys. Anal. Geom., 9, 53, 10.1007/s11040-005-9002-8