Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Steven M. Gonek"'
Autor:
Steven M. Gonek, Fan Ge
Publikováno v:
Transactions of the American Mathematical Society. 373:4713-4734
We study the mean square of the error term, or the mean square discrepancy, in the Dirichlet divisor problem. An analysis of the off-diagonal terms in the mean square of the Voronoi summation formula leads to a precise conjecture for this mean square
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ccbacd27ab246ed1399368af1c57dd4a
https://doi.org/10.1090/tran/8087
https://doi.org/10.1090/tran/8087
Publikováno v:
Proceedings of the American Mathematical Society. 148:2863-2875
We recast the classical Lindelöf hypothesis as an estimate for the sums ∑ n ≤ x n − i t \sum _{n\leq x}n^{-it} . This leads us to propose that a more general form of the Lindelöf hypothesis may be true, one involving estimates for sums of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba5608c6601e2181592743623e4d5b4b
https://doi.org/10.1090/proc/14974
https://doi.org/10.1090/proc/14974
Autor:
Steven M. Gonek, Siegfred Baluyot
Publikováno v:
Pacific Journal of Mathematics. 303:47-71
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::699789ead443728b92570276d7e70334
https://doi.org/10.2140/pjm.2019.303.47
https://doi.org/10.2140/pjm.2019.303.47
Autor:
Haseo Ki, Steven M. Gonek
Publikováno v:
Journal of Number Theory. 186:35-61
We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ ( s ) , and 0 a 1 / 2 , then all but a finite number of the zeros of ℜ ζ ( a + i t ) , ℑ ζ ( a + i t ) , and similar functions are simple. We also study the pair c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a7548384acdf58ca13f8db021a30cd5c
https://doi.org/10.1016/j.jnt.2017.10.024
https://doi.org/10.1016/j.jnt.2017.10.024
Publikováno v:
Andrade, J C, Gonek, S M & Keating, J 2018, ' Truncated Product Representations for L-Functions in the Hyperelliptic Ensemble ', Mathematika, vol. 64, no. 1, pp. 137-158 . https://doi.org/10.1112/S0025579317000407
We investigate the approximation of quadratic Dirichlet $L$-functions over function fields by truncations of their Euler products. We first establish representations for such $L$-functions as products over prime polynomials times products over their
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e211efae683e2304b2cd2e2c3a2c2713
https://doi.org/10.1112/s0025579317000407
https://doi.org/10.1112/s0025579317000407
Autor:
Steven M. Gonek, Alex Iosevich
Publikováno v:
Mosc. J. Comb. Number Theory 8, no. 3 (2019), 263-287
We study the mean square of the error term in the Gauss circle problem. A heuristic argument based on the consideration of off-diagonal terms in the mean square of the relevant Voronoi-type summation formula leads to a precise conjecture for the mean
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a9714583cce16fbd0c701c3d8d01315
https://projecteuclid.org/euclid.moscow/1565661750
https://projecteuclid.org/euclid.moscow/1565661750
Autor:
Steven M. Gonek, Yoonbok Lee
Publikováno v:
The Quarterly Journal of Mathematics. 68:301-344
We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients in the vertical strip $\sigma_\mathit1\mathit \il \mathfrak Rs\mathit \lt \sigma_\mathit2$ , where $1/2\lt \sigma_1\lt \s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1b35315d751c00d032a3bd1c63aa272d
https://doi.org/10.1093/qmath/haw041
https://doi.org/10.1093/qmath/haw041
Autor:
H. L. Montgomery, Steven M. Gonek
Publikováno v:
The Quarterly Journal of Mathematics. 67:483-505
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::54e953179dd8f3db60613b6c45e53913
https://doi.org/10.1093/qmath/haw022
https://doi.org/10.1093/qmath/haw022
Autor:
Hugh L. Montgomery, Steven M. Gonek
Publikováno v:
Indagationes Mathematicae. 27:506-523
We review the various proofs of Kronecker’s theorem concerning inhomogeneous Diophantine approximation, we discuss in detail the quantitative approaches of Turan (1960) and Chen (2000), and we derive strong localized versions of these theorems.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a3f7555ee89c95980163a39c3dbff085
https://doi.org/10.1016/j.indag.2016.02.002
https://doi.org/10.1016/j.indag.2016.02.002
Autor:
Steven M. Gonek
Publikováno v:
Proceedings of the American Mathematical Society. 143:3295-3302
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::90a67b30914628d361b1cca408a656b6
https://doi.org/10.1090/proc/12380
https://doi.org/10.1090/proc/12380