On the Discretized Li Coefficients for a Certain Class of $$L-$$Functions

Bulletin of the Malaysian Mathematical Sciences Society - Tập 44 Số 6 - Trang 3601-3627 - 2021
Almasa Odžak1, Medina Zubača1
1Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71000, Sarajevo, Bosnia and Herzegovina

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Tài liệu tham khảo

Li, X.J.: The positivity of a sequence of numbers and the Riemann hypothesis. J. Number Theory 65(2), 325–333 (1997)

Keiper, J.: Power series expansions of Riemann’s $$\xi $$ function. Math. Comput. 58, 765–773 (1992). https://doi.org/10.1090/S0025-5718-1992-1122072-5

Maślanka, K.: Li’s criterion for the Riemann hypothesis–numerical approach. Opuscula Math. 24, 103–114 (2004)

Voros, A.: Sharpenings of Li’s criterion for the Riemann hypothesis. Math. Phys. Anal. Geom. 9, 53–63 (2006)

Mazhouda, K., Omar, S., Ouni, R.: On the Li coefficients for the Hecke $$L$$-functions. Math. Phys. Anal. Geom. 17, 67–81 (2014). https://doi.org/10.1007/s11040-014-9141-x

Lagarias, J.: Li coefficients for automorphic $$L$$-functions. Ann. Inst. Fourier 57, 1689–1740 (2007). https://doi.org/10.5802/aif.2311

Odžak, A., Smajlović, L.: On asymptotic behavior of generalized Li coefficients in the Selberg class. J. Number Theory 131, 519–535 (2011). https://doi.org/10.1016/j.jnt.2010.08.009

Smajlović, L.: On Li’s criterion for the Riemann hypothesis for the Selberg class. J. Number Theory 130, 828–851 (2010). https://doi.org/10.1016/j.jnt.2009.10.012

Odžak, A., Smajlović, L.: On Li’s coefficients for the Rankin-Selberg $$L$$-functions. Ramanujan J. 21, 303–334 (2010). https://doi.org/10.1007/s11139-009-9175-z

Freitas, P.: A Li-type criterion for zero-free half-planes of Riemann’s zeta function. J. Lond. Math. Soc. 73(2), 399–414 (2006). https://doi.org/10.1112/S0024610706022599

Sekatskii, S.K.: Generalized Bombieri-Lagarias’ theorem and generalized Li’s criterion with its arithmetic interpretation. Ukr. Mat. Zh. 66, 371–383 (2014)

Bucur, A., Ernvall-Hytönen, A.M., Odžak, A., Roditty-Gershon, E., Smajlović, L.: On $$\tau $$ - Li coefficients for Rankin-Selberg $$L$$-functions. In: Bertin, M.J., Bucur, A., Feigon, B., Schneps, L. (eds.) Women in Numbers Europe, pp. 167–190. Springer, Switzerland (2015)

Droll, A.: Variations of Li’s criterion for an extension of the Selberg class. PhD thesis, Queen’s University Ontario, Canada (2012). http://hdl.handle.net/1974/7352

Ernvall-Hytönen, A.M., Odžak, A., Smajlović, L., Sušić, M.: On the modified Li criterion for a certain class of $$L$$-functions. J. Number Theory 156, 340–367 (2015). https://doi.org/10.1016/j.jnt.2015.03.019

Bucur, A., Ernvall-Hytönen, A.M., Odžak, A., Smajlović, L.: On a Li-type criterion for zero-free regions of certain Dirichlet series with real coefficients. LMS J. Comput. Math. 19(1), 259–280 (2016). https://doi.org/10.1112/S1461157016000115

Odžak, A.: On the asymptotic criterion for the zero-free regions of certain $$L$$-functions. Turk. J. Math. 40, 688–702 (2016). https://doi.org/10.3906/mat-1410-41

Voros, A.: Discretized Keiper/Li approach to the Riemann hypothesis. Exp. Math.1–18 (2018). https://doi.org/10.1080/10586458.2018.1482480

Ernvall-Hytönen, A.M., Odžak, A., Sušić, M.: On asymptotic behavior of generalized Li coefficients. Taiwanese J. Math. 22(6), 1321–1346 (2018)

Davenport, H.: Multiplicative Number Theory. 74. Springer, New York (2000)

Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 55. NBS Applied Mathematics Series, Washington (1964)

Bender, C.M., Orszag, S.A.: Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill (1978)

Luke, Y.L.: The Special Functions and Their Approximations. Elsevier Science (1969). https://books.google.ba/books?id=huuO6mKbVoEC

Falck, E.: Asymptotic expansions of integrals and the method of steepest descent. Uppsala University (2016). https://uu.divaportal.org/smash/get/diva2:1058214/FULLTEXT01.pdf

Johansson, F.: Arb: a C library for ball arithmetic. ACM Commun. Comput. Algebra 47(4), 166–169 (2013). https://doi.org/10.1145/2576802.2576828