Add to ORKGUpdated time Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel zeros—certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of Dirichlet L-functions at the central point
We estimate the 1-level density of low-lying zeros of L(s,χ) with χ ranging over primitive Dirichlet...
Let be a real primitive character modulo D. If the L-function (,) has a real zero close to =1, know...
AbstractAssuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros...
The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,...
Let $\chi$ be a real primitive character to the modulus $D$. It is proved that $$ L(1,\chi)\gg (\log...
Under the assumption of infinitely many Siegel zeroes $s$ with $Re(s)>1-\frac{1}{(\log q)^{r^r}}$ fo...
AbstractWe show that if the derivative of the Riemann zeta function has sufficiently many zeros clos...
Let $q$ be a prime, $\chi$ be a non-principal Dirichlet character $\bmod\ q$ and $L(s,\chi)$ be the...
Thesis (MSc)--Stellenbosch University, 2019.ENGLISH ABSTRACT: Please refer to full text for abstract...
AbstractTextOne of the most important statistics in studying the zeros of L-functions is the 1-level...
In the paper, we obtain that certain linear and more general combinations of Dirichlet L-functions a...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42024/1/222-150-1-1_21500001.pd
The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function....
The Riemann zeta function has a deep connection to the distribution of primes. In 1911 Landau proved...
AbstractWe examine the connections between small zeros of quadratic L-functions, Chebyshev's bias, a...
We estimate the 1-level density of low-lying zeros of L(s,χ) with χ ranging over primitive Dirichlet...
Let be a real primitive character modulo D. If the L-function (,) has a real zero close to =1, know...
AbstractAssuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros...
The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,...
Let $\chi$ be a real primitive character to the modulus $D$. It is proved that $$ L(1,\chi)\gg (\log...
Under the assumption of infinitely many Siegel zeroes $s$ with $Re(s)>1-\frac{1}{(\log q)^{r^r}}$ fo...
AbstractWe show that if the derivative of the Riemann zeta function has sufficiently many zeros clos...
Let $q$ be a prime, $\chi$ be a non-principal Dirichlet character $\bmod\ q$ and $L(s,\chi)$ be the...
Thesis (MSc)--Stellenbosch University, 2019.ENGLISH ABSTRACT: Please refer to full text for abstract...
AbstractTextOne of the most important statistics in studying the zeros of L-functions is the 1-level...
In the paper, we obtain that certain linear and more general combinations of Dirichlet L-functions a...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42024/1/222-150-1-1_21500001.pd
The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function....
The Riemann zeta function has a deep connection to the distribution of primes. In 1911 Landau proved...
AbstractWe examine the connections between small zeros of quadratic L-functions, Chebyshev's bias, a...
We estimate the 1-level density of low-lying zeros of L(s,χ) with χ ranging over primitive Dirichlet...
Let be a real primitive character modulo D. If the L-function (,) has a real zero close to =1, know...
AbstractAssuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros...