Results 11 to 20 of about 86 (74)
Extreme values of derivatives of zeta and L-functions. [PDF]
Bull Lond Math SocAbstract It is proved that as T→∞$T \rightarrow \infty$, uniformly for all positive integers ℓ⩽(log3T)/(log4T)$\ell \leqslant (\log _3 T) / (\log _4 T)$, we have maxT⩽t⩽2Tζ(ℓ)1+it⩾Yℓ+o1log2Tℓ+1,$$\begin{equation*} \hspace*{1.5pc}\max _{T\leqslant t\leqslant 2T}{\left|\zeta ^{(\ell )}{\left(1+it\right)}\right|} \geqslant {\left({\mathbf {Y}_{\ell }}+ o{\
Yang D.
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Aspects of the screw function corresponding to the Riemann zeta‐function
Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023 Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
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Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$
Mathematika, Volume 69, Issue 4, Page 1081-1103, October 2023., 2023 Abstract We establish lower bounds for the discrete 2kth moment of the derivative of the Riemann zeta function at nontrivial zeros for all k<0$k<0$ under the Riemann hypothesis and the assumption that all zeros of ζ(s)$\zeta (s)$ are simple.
Peng Gao, Liangyi Zhao
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Multiplicative functions in short arithmetic progressions
Proceedings of the London Mathematical Society, Volume 127, Issue 2, Page 366-446, August 2023., 2023 Abstract We study for bounded multiplicative functions f$f$ sums of the form ∑n⩽xn≡a(modq)f(n),$$\begin{align*} \hspace*{7pc}\sum _{\substack{n\leqslant x\\ n\equiv a\ (\mathrm{mod}\ q)}}f(n), \end{align*}$$establishing that their variance over residue classes a(modq)$a \ (\mathrm{mod}\ q)$ is small as soon as q=o(x)$q=o(x)$, for almost all moduli q$q$,
Oleksiy Klurman +2 more
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The elliptic sieve and Brauer groups
Proceedings of the London Mathematical Society, Volume 126, Issue 6, Page 1884-1922, June 2023., 2023 Abstract A theorem of Serre states that almost all plane conics over Q${{\mathbb {Q}}}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves.
Subham Bhakta +3 more
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Study of the generalized von mangoldt function defined by L-additive function
, 2023 14 ...
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Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges
Proceedings of the London Mathematical Society, 2018 80 pages, no figures.
Matomäki, Kaisa +2 more
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Quantitative asymptotics for polynomial patterns in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We prove quantitative estimates for averages of the von Mangoldt and Möbius functions along polynomial progressions n+P1(m),…,n+Pk(m)$n+P_1(m),\ldots, n+P_k(m)$ for a large class of polynomials Pi$P_i$. The error terms obtained save an arbitrary power of logarithm, matching the classical Siegel–Walfisz error term.
Lilian Matthiesen +2 more
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Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract Under the generalized Riemann hypothesis, we use Beurling–Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet L$L$‐functions for a large prime modulus q$q$. As applications, we give alternative proofs of several results on low‐lying zeros of L(s,χ)$L(s,\chi)$ and obtain a new lower bound on the proportion ...
Tianyu Zhao
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Explicit height estimates for CM curves of genus 2
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey +2 more
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