Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Brad Rodgers"'
Autor:
BRAD RODGERS, TERENCE TAO
Publikováno v:
Forum of Mathematics, Pi, Vol 8 (2020)
For each $t\in \mathbb{R}$, we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function $$\
Externí odkaz:
https://doaj.org/article/6a13165ce7ee4f4c821c8a0c70debfd6
Publikováno v:
Geometric and Functional Analysis. 31:111-149
We evaluate asymptotically the variance of the number of squarefree integers up to $x$ in short intervals of length $H < x^{6/11 - \varepsilon}$ and the variance of the number of squarefree integers up to $x$ in arithmetic progressions modulo $q$ wit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab32de9590f2fcba75b9d73ad15821ad
https://doi.org/10.1007/s00039-021-00557-5
https://doi.org/10.1007/s00039-021-00557-5
Autor:
Ofir Gorodetsky, Brad Rodgers
Publikováno v:
American Journal of Mathematics. 143:1703-1745
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9556096b2625b5a6e8f347b2c0ee598c
https://doi.org/10.1353/ajm.2021.0044
https://doi.org/10.1353/ajm.2021.0044
Autor:
Terence Tao, Brad Rodgers
Publikováno v:
Forum of Mathematics, Pi. 8
For each $t\in \mathbb{R}$ , we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5427ecb0c1aba332c4f6d1ebc703d43e
https://doi.org/10.1017/fmp.2020.6
https://doi.org/10.1017/fmp.2020.6
Autor:
Brad Rodgers
Publikováno v:
Algebra Number Theory 12, no. 5 (2018), 1243-1279
We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements of $\mathbb{F}_q[T]$ into primes and the factorizations of random permu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc80fc224c7a409c081a3cd4c1635c33
https://doi.org/10.2140/ant.2018.12.1243
https://doi.org/10.2140/ant.2018.12.1243
Publikováno v:
Mathematische Zeitschrift. 288:167-198
We study the mean square of sums of the kth divisor function $$d_k(n)$$ over short intervals and arithmetic progressions for the rational function field over a finite field of q elements. In the limit as $$q\rightarrow \infty $$ we establish a relati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2adbfdb7919ff0536584fc7a162b79f9
https://doi.org/10.1007/s00209-017-1884-1
https://doi.org/10.1007/s00209-017-1884-1
Autor:
Brad Rodgers, Ofir Gorodetsky
Publikováno v:
Transactions of the American Mathematical Society
Let $M$ be a random matrix chosen according to Haar measure from the unitary group $\mathrm{U}(n,\mathbb{C})$. Diaconis and Shahshahani proved that the traces of $M,M^2,\ldots,M^k$ converge in distribution to independent normal variables as $n \to \i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ab31af9ea8f2a821f72cff7a367795a
Autor:
Jeffrey C. Lagarias, Brad Rodgers
The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between nontrivial zeros is suppos
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::428c3ae81895d612768114b092f71941
Autor:
Kenneth Maples, Brad Rodgers
Publikováno v:
International Journal of Number Theory. 11:2087-2107
We unconditionally prove a central limit theorem for linear statistics of the zeros of the Riemann zeta function with diverging variance. Previously, theorems of this sort have been proved under the assumption of the Riemann hypothesis. The result mi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d29cb386b6524521409f96db5c1489c
https://doi.org/10.1142/s1793042115500918
https://doi.org/10.1142/s1793042115500918
We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the Gaussian Unitary
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::145bb1fb9ab01491e931392ea3c7f573