H. M. Bui
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
H. M. Bui has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Micah B. Milinovich
Department of Mathematics, University of Mississippi, University, Mississippi 38677
3 shared publications - John Brian Conrey
American Institute of Mathematics, Pasadena, USA
2 shared publications - Matthew P. Young
Department of Mathematics, Rutgers University, NJ, USA
2 shared publications - N. Ng
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada T1K 3M4
2 shared publications - David Rodney Heath-Brown
Mathematical Institute Oxford
1 shared publication
Latest Publications
- Open Access
More than 41% of the zeros of the zeta function are on the critical line
We prove that more than 41% of the zeros of the zeta function are on the critical line.
Open AccessMore than 41% of the zeros of the zeta function are on the critical line
We prove that more than 41% of the zeros of the zeta function are on the critical line.
- 1 January 2011
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 150 (1) , 35-64
More than 41% of the zeros of the zeta function are on the critical line
We prove that more than 41% of the zeros of the zeta function are on the critical line.Comment: 23 pages; v2: added a new paragraph on pp.1-2, minor correction
- 1 January 2011
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- Vol. 150 (1) , 35-64
More than 41% of the zeros of the zeta function are on the critical line
We prove that more than 41% of the zeros of the zeta function are on the critical line.Comment: 23 pages; v2: added a new paragraph on pp.1-2, minor correction
- Open Access
Non-vanishing of Dirichlet L-functions at the central point
Let $\chi$ be a primitive Dirichlet character modulo $q$ and $L(s,\chi)$ be the Dirichlet L-function associated to $\chi$. Using a new two-piece mollifier we show that $L(\tfrac{1}{2},\chi)\ne0$ for at least 34% of the characters in the family.Open AccessNon-vanishing of Dirichlet L-functions at the central point
Let $\chi$ be a primitive Dirichlet character modulo $q$ and $L(s,\chi)$ be the Dirichlet L-function associated to $\chi$. Using a new two-piece mollifier we show that $L(\tfrac{1}{2},\chi)\ne0$ for at least 34% of the characters in the family. - Open Access
Large gaps between consecutive zeros of the Riemann zeta-function
Combining the mollifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist infinitely many consecutive gaps greater than 3.033 times the average spacing.
Open AccessLarge gaps between consecutive zeros of the Riemann zeta-function
Combining the mollifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist infinitely many consecutive gaps greater than 3.033 times the average spacing.
- Open Access
- 28 May 2010
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 138 (12) , 4167-4175
A note on the gaps between consecutive zeros of the Riemann zeta-function
Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and that infinitely often they differ by at least 2.6950 times the average spacing.
- 28 May 2010
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 138 (12) , 4167-4175
Open AccessA note on the gaps between consecutive zeros of the Riemann zeta-function
Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and that infinitely often they differ by at least 2.6950 times the average spacing.
- 10 December 2009
- Published by Wiley in Mathematika
- Vol. 56 (1) , 35-44
A NOTE ON THE SECOND MOMENT OF AUTOMORPHIC L ‐FUNCTIONS
- 10 December 2009
- Published by Wiley in Mathematika
- Vol. 56 (1) , 35-44
A NOTE ON THE SECOND MOMENT OF AUTOMORPHIC L ‐FUNCTIONS
- Open Access
Central values of derivatives of Dirichlet L-functions
Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).
Open AccessCentral values of derivatives of Dirichlet L-functions
Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).
- Open Access
A note on the gaps between consecutive zeros of the Riemann zeta-function
Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.
Open AccessA note on the gaps between consecutive zeros of the Riemann zeta-function
Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.
- Open Access
A note on the second moment of automorphic L-functions
We obtain the formula for the twisted harmonic second moment of the $L$-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet $L$-functions.
Open AccessA note on the second moment of automorphic L-functions
We obtain the formula for the twisted harmonic second moment of the $L$-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet $L$-functions.
- Open Access
A note on the fourth moment of Dirichlet L-functions
We prove an asymptotic formula for the fourth power mean of Dirichlet L-functions averaged over primitive characters to modulus q and over t\in [0,T] which is particularly effective when q \ge T. In this range the correct order of magnitude was not previously known.
Open AccessA note on the fourth moment of Dirichlet L-functions
We prove an asymptotic formula for the fourth power mean of Dirichlet L-functions averaged over primitive characters to modulus q and over t\in [0,T] which is particularly effective when q \ge T. In this range the correct order of magnitude was not previously known.