Zeros of partial sums of L-functions

Balanzario, 2000, On Dirichlet polynomial approximations to the Riemann zeta function, vol. 27, 3 Bombieri, 1997, Remarks on the analytic complexity of zeta functions, vol. 247, 21 Bombieri, 1995, Dirichlet polynomial approximations to zeta functions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 22, 517 Borwein, 2007, Zeros of partial sums of the Riemann zeta function, Exp. Math., 16, 21, 10.1080/10586458.2007.10128981 Burgeĭn, 2012, Uniform approximation of a partial sum by a shorter sum and Φ-widths, Mat. Sb., 203, 57 Cojocaru, 2006, An Introduction to Sieve Methods and Their Applications, vol. 66 Drappeau Elliott, 1980, Probabilistic Number Theory: Central Limit Theorems, vol. 240 Goldmakher, 2012, Multiplicative mimicry and improvements to the Pólya–Vinogradov inequality, Algebra Number Theory, 6, 123, 10.2140/ant.2012.6.123 Gonek, 2010, Zeros of partial sums of the Riemann zeta-function, Int. Math. Res. Not., 1775 Granville, 2015, What is the best approach to counting primes?, 83 Granville, 2018, A more intuitive proof of a sharp version of Halász's theorem, Proc. Amer. Math. Soc., 146, 4099, 10.1090/proc/14095 Granville, 2019, A new proof of Halász's theorem, and its consequences, Compos. Math., 155, 126, 10.1112/S0010437X18007522 Granville Granville Granville, 2007, Large character sums: pretentious characters and the Pólya–Vinogradov theorem, J. Amer. Math. Soc., 20, 357, 10.1090/S0894-0347-06-00536-4 Halász, 1968, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hung., 19, 365, 10.1007/BF01894515 Halász, 1971, On the distribution of additive and the mean values of multiplicative arithmetic functions, Studia Sci. Math. Hungar., 6, 211 Hardy, 1929, The approximate functional equation for ζ(s) and ζ2(s), Proc. Lond. Math. Soc. (2), 29, 81, 10.1112/plms/s2-29.1.81 Hiary, 2011, A nearly-optimal method to compute the truncated theta function, its derivatives, and integrals, Ann. of Math. (2), 174, 859, 10.4007/annals.2011.174.2.3 Hiary, 2011, Fast methods to compute the Riemann zeta function, Ann. of Math. (2), 174, 891, 10.4007/annals.2011.174.2.4 Hiary, 2014, Computing Dirichlet character sums to a power-full modulus, J. Number Theory, 140, 122, 10.1016/j.jnt.2013.12.005 Iwaniec, 2004, Analytic Number Theory, vol. 53 Lamzouri Landau, 1949 Langer, 1931, On the zeros of exponential sums and integral, Bull. Amer. Math. Soc., 37, 213, 10.1090/S0002-9904-1931-05133-8 Ledoan, 2014, Zeros of partial sums of the Dedekind zeta function of a cyclotomic field, J. Number Theory, 136, 118, 10.1016/j.jnt.2013.09.003 Mine Monach, 1980 Montgomery, 1978 Montgomery, 1983, Zeros of Approximations to the Zeta Function, 497 Montgomery, 1973, The large sieve, Mathematika, 20, 119, 10.1112/S0025579300004708 Montgomery, 1974, Hilbert's inequality, J. Lond. Math. Soc. (2), 8, 73, 10.1112/jlms/s2-8.1.73 Montgomery, 2001, Mean values of multiplicative functions, Period. Math. Hungar., 43, 199, 10.1023/A:1015202219630 Montgomery, 2007, Multiplicative Number Theory. I. Classical Theory, vol. 97 Murty, 2002, Sieving using Dirichlet series, 111 Murty, 2005, Problems in Algebraic Number Theory, vol. 190 Platt, 2016, Zeroes of partial sums of the zeta-function, LMS J. Comput. Math., 19, 37, 10.1112/S1461157015000340 Pólya, 1998, Problems and theorems in analysis Raikov, 1938, Generalisation of a theorem of Ikehara–Landau, Mat. Sb., 45, 559 A. Roy, A. Vatwani, Zeros of Dirichlet polynomials, preprint. Shiu, 1980, A Brun–Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math., 313, 161 Spira, 1966, Zeros of sections of the zeta function. I, Math. Comp., 20, 542, 10.1090/S0025-5718-1966-0203910-1 Spira, 1968, Zeros of sections of the zeta function. II, Math. Comp., 22, 163, 10.1090/S0025-5718-1968-0228456-8 J.D. Tamarkin, Some General Problems in the Theory of Ordinary Linear Differential Equations, Petrograd, 1917. Tamarkin, 1927, Math. Z., 27, 24 Tenenbaum, 2015, Introduction to Analytic and Probabilistic Number Theory, vol. 163 Tenenbaum, 2017, Moyennes effectives de fonctions multiplicatives complexes, Ramanujan J., 44, 641, 10.1007/s11139-017-9949-7 Titchmarsh, 1986 Turán, 1948, On some approximative Dirichlet-polynomials in the theory of the zeta-function of Riemann, Danske Vid. Selsk. Mat.-Fys. Medd., 24 Turán, 1959, Nachtrag zu meiner Abhandlung “On some approximative Dirichlet polynomials in the theory of zeta-function of Riemann”, Acta Math. Acad. Sci. Hung., 10, 277, 10.1007/BF02024493 Turán, 1960, A theorem on diophantine approximation with application to Riemann zeta-function, Acta Sci. Math. (Szeged), 21, 311 van de Lune, 2010, Numerical computation of special zeros of partial sums of Riemann's zeta function, vol. 155, 371 Wilder, 1917, Expansion problems of ordinary linear differential equations with auxiliary conditions at more than two points, Trans. Amer. Math. Soc., 18, 415, 10.1090/S0002-9947-1917-1501077-6 Wintner, 1942, On the prime number theorem, Amer. J. Math., 64, 320, 10.2307/2371686 Wirsing, 1967, Das asymptotische Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung., 18, 414, 10.1007/BF02280301