Zeros of Partial Sums of the Riemann Zeta Function

Borwein, Peter; Fee, G. J.; Ferguson, Roger; Waall, Alexa van der

doi:10.1080/10586458.2007.10128981

Cited by 29 publications

(32 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…From the two previous results we obtain a property about the bound b n , de…ned in (2.4), which allows inter alia to complete a result obtained by Borwein et al [4,Theorem 4.7].…”

Section: Introductionsupporting

confidence: 49%

See 1 more Smart Citation

On the asymptotically uniform distribution of the zeros of the partial sums of the Riemann zeta function

Mora

2013

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…From the two previous results we obtain a property about the bound b n , de…ned in (2.4), which allows inter alia to complete a result obtained by Borwein et al [4,Theorem 4.7].…”

Section: Introductionsupporting

confidence: 49%

“…By taking n 0 = p (4) , we claim that if n > n 0 then (2.24) is true. Indeed, since n > p (4) we have p kn 3 p (1) and then by applying four times (2.25), there exist four primes p, q, r and s such that…”

Section: Lemmamentioning

confidence: 99%

On the asymptotically uniform distribution of the zeros of the partial sums of the Riemann zeta function

Mora

2013

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…However, the weaker statement is sufficient for our purposes and we do not pursue this line of thought further. 3 Note that this covered a wider interval than was strictly necessary. 4 A single node of Phase III contains two 8-core Intel E5-2670 Sandybridge processors running at 2.6GHz.…”

Section: 3mentioning

confidence: 99%

Zeroes of partial sums of the zeta-function

Platt¹,

Trudgian

2016

LMS J. Comput. Math.

View full text Add to dashboard Cite

show abstract

“…Zeros of ζ N (s) have been widely studied and various other results are known in the literature due to a number of mathematicians. Among these, we refer the reader to Borwein, Fee, Ferguson and Waall [4], Gonek and Ledoan [9], Langer [20] and Wilder [44].…”

Section: Introductionmentioning

confidence: 99%

Zeros of partial sums of L-functions

Roy

Vatwani

2019

Advances in Mathematics

View full text Add to dashboard Cite

We consider a certain class of multiplicative functions f : N → C. Let F (s) = ∞ n=1 f (n)n −s be the associated Dirichlet series and FN (s) = n≤N f (n)n −s be the truncated Dirichlet series. In this setting, we obtain new Halász-type results for the logarithmic mean value of f . More precisely, we prove estimates for the sum x n=1 f (n)/n in terms of the size of |F (1 + 1/ log x)| and show that these estimates are sharp. As a consequence of our mean value estimates, we establish non-trivial zero-free regions for these partial sums FN (s).In particular, we study the zero distribution of partial sums of the Dedekind zeta function of a number field K. More precisely, we give some improved results for the number of zeros upto height T as well as new zero density results for the number of zeros up to height T , lying to the right of Re(s) = σ, where σ ≥ 1/2.

show abstract

Zeros of Partial Sums of the Riemann Zeta Function

Cited by 29 publications

References 0 publications

On the asymptotically uniform distribution of the zeros of the partial sums of the Riemann zeta function

On the asymptotically uniform distribution of the zeros of the partial sums of the Riemann zeta function

Zeroes of partial sums of the zeta-function

Zeros of partial sums of L-functions

Contact Info

Product

Resources

About