By Kálmán Györy;Gergely Harcos;József Szabados;Miklós Simonovits;János Pintz;All authors
Paul Turan, one of many maximum Hungarian mathematicians, used to be born a hundred years in the past, on August 18, 1910. To have fun this celebration the Hungarian Academy of Sciences, the Alfred Renyi Institute of arithmetic, the Janos Bolyai Mathematical Society and the Mathematical Institute of Eotvos Lorand college prepared a global convention dedicated to Paul Turan's major components of curiosity: quantity conception, chosen branches of study, and chosen branches of combinatorics. The convention was once held in Budapest, August 22-26, 2011. a number of the invited lectures reviewed various points of Paul Turan's paintings and impression. many of the lectures allowed members to file approximately their very own paintings within the above pointed out components of arithmetic
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Additional resources for Number Theory, Analysis, and Combinatorics : Proceedings of the Paul Turan Memorial Conference held August 22-26, 2011 in Budapest
Brändén , J. Borcea and P. Brändén [16, 17, 18, 19, 20] and B. Shapiro . 4 Loca tion of zeros and Hermite expansions. In Section 3 (entitled Fourier transforms and the Riemann ????-function), we cite results which show that the Taylor coefficients of entire 26 | George Csordas functions represented by Fourier transforms of certain kernels also satisfy the Turán inequalities. The paper also includes a number of open problems. For the interested reader, and for the sake of brevity, each subsection includes a list of recommended collateral readings.
Preliminaries aside, we are now in position to state the following theorem. 1]). Let ????(????) = ????−???????? ????1 (????), where the genus of the real entire function ????1 (????) is 0 or 1, ????1 (????) ≢ 0 and ???? ≥ 0. Let ????(????) and ???? ???? (????) denote the functions defined above (see (6)). Then ????(????) ∈ L-P if and only if ???? ???? (????) ≥ 0 for all ???? ∈ ℝ and ???? ∈ ℕ0 . 9]. Conjecture 10. Let ????(????) be a real entire function, ????(????) ≢ 0. Let ????(????) and ???? ???? (????) denote the functions defined above (see (6)). If ???? ???? (????) ≥ 0 for all ???? ∈ ℝ and ???? ∈ ℕ0 , then ????(????) ∈ L-P.
Soc. 9. M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 155–164. A. E. Ingham, On the estimation of ????(????, ????), Quart. J. Math. 11 (1940), 291–292. P. X. Gallagher, The large sieve, Mathematika, 14 (1967), 14–20. P. Turán, On a New Method of Analysis and its Applications, Pure and Applied Mathematics, John Wiley and Sons, New York, 1984. R. Balasubramanian and K. Ramachandra, On the zeros of the Riemann zeta-function and L-series, II, Hardy–Ramanujan J. 5 (1982), 1–30.