On the Real $\tau$-Conjecture and the Distribution of Complex Roots
by Pavel Hrubeš
Theory of Computing, Volume 9(10), pp. 403-411, 2013
Bibliography with links to cited articles
[1] Peter Bürgisser: On defining integers and proving arithmetic circuit lower bounds. Comput. Complexity, 18(1):81–103, 2009. Preliminary version in STACS’07. [doi:10.1007/s00037-009-0260-x]
[2] Paul Erds and Pál Turán: On the distribution of roots of polynomials. Ann. of Math., 51(1):105–119, 1950. JSTOR.
[3] Walter K. Hayman: Angular value distribution of power series with gaps. Proc. London Mathematical Society, s3-24(4):590–624, 1972. [doi:10.1112/plms/s3-24.4.590]
[4] Aubrey J. Kempner: On the complex roots of algebraic equations. Bull. Amer. Math. Soc., 41(12):809–843, 1935. [doi:10.1090/S0002-9904-1935-06201-9]
[5] Askold G. Khovanskii: Fewnomials. Volume 88 of Translations of Mathematical Monographs. Amer. Math. Soc., 1991.
[6] Pascal Koiran: Shallow circuits with high-powered inputs. In Proc. 2nd Symp. Innovations in Computer Science (ICS’11), pp. 309–320. Tsinghua University Press, 2011. ICS’11.
[7] Pascal Koiran, Natacha Portier, and Sébastien Tavenas: A Wronskian approach to the real τ-conjecture. Preprint, 2012. [arXiv:1205.1015]
[8] Nikola Obreschkoff: Über die Wurzeln algebraischer Gleichungen. Jahresbericht der Deutschen Mathematiker-Vereinigung, 33:52–64, 1925. DigiZeitschriften.
[9] Qazi I. Rahman and Gerhard Schmeisser: Analytic Theory of Polynomials. Oxford Univ. Press, 2002.
[10] Jean-Jacques Risler: Additive complexity and zeros of real polynomials. SIAM J. Comput., 14(1):178–183, 1985. [doi:10.1137/0214014]
[11] Michael Shub and Steve Smale: On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “NP≠P?”. Duke Mathematical Journal, 81(1):47–54, 1995. [doi:10.1215/S0012-7094-95-08105-8]
[12] Steve Smale: Mathematical problems for the next century. The Mathematical Intelligencer, 20(2):7–15, 1998. [doi:10.1007/BF03025291]