Results 21 to 30 of about 2,061 (84)

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, Samuel Le Fourn, Elisa Lorenzo García   +2 more
wiley   +1 more source

Topology of complete Finsler manifolds with radial flag curvature bounded below

, 2013
We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution (arXiv:1205.3913).
Kondo, Kei, Ohta, Shin-ichi, Tanaka, Minoru   +2 more
core   +1 more source

Simple Barban–Davenport–Halberstam type asymptotics for general sequences

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract We prove two estimates for the Barban–Davenport–Halberstam type variance of a general complex sequence in arithmetic progressions. The proofs are elementary, and our estimates are capable of yielding an asymptotic for the variance when the sequence is sufficiently nice, and is either somewhat sparse or is sufficiently like the integers in its ...
Adam J. Harper
wiley   +1 more source

Moments of the Riemann zeta function at its local extrema

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non‐trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of the Riemann zeta function evaluated at its local extrema along the critical line to leading order.
Andrew Pearce‐Crump
wiley   +1 more source

Counting primes with a given primitive root, uniformly

Mathematika, Volume 71, Issue 4, October 2025.
Abstract The celebrated Artin conjecture on primitive roots asserts that given any integer g$g$ that is neither −1$-1$ nor a perfect square, there is an explicit constant A(g)>0$A(g)>0$ such that the number Π(x;g)$\Pi (x;g)$ of primes p⩽x$p\leqslant x$ for which g$g$ is a primitive root is asymptotically A(g)π(x)$A(g)\pi (x)$ as x→∞$x\rightarrow \infty$
Kai (Steve) Fan, Paul Pollack
wiley   +1 more source

Large Nc QCD and Harmonic Sums

, 2011
In the Large-Nc limit of QCD, two--point functions of local operators become Harmonic Sums. I review some properties which follow from this fact and which are relevant for phenomenological applications.
A Manohar, C Vafa, C Vafa, D Espriu, D Greynat, E Rafael de, E Rafael de, E Witten, E Witten, E Witten, EDUARDO DE RAFAEL, G Ecker, G Ecker, Gt’ Hooft, G’t Hooft, J Bijnens, J Comellas, J Gasser, J Wess, J-Ph Aguilar, JF Donoghue, M Golterman, M Gonzalez-Alonso, M Knecht, M Knecht, MA Shifman, O Catà, P Masjuan, Ph Flajolet, S Coleman, S Friot, S Peris, S Weinberg, S Weinberg, T Das, T Hambye, V Cirigliano, Y Nambu   +37 more
core   +3 more sources

Odd moments and adding fractions

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract We prove near‐optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an application, we prove near‐optimal upper bounds for the average of the refined singular series in the Hardy–Littlewood conjectures concerning the number of prime k$k$‐tuples
Thomas F. Bloom, Vivian Kuperberg
wiley   +1 more source

On the second moment for primes in an arithmetic progression

, 2000
Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged
Goldston, Daniel, Yildirim, C. Y.
core   +2 more sources

Smallest totient in a residue class

Bulletin of the London Mathematical Society, Volume 57, Issue 6, Page 1908-1917, June 2025.
Abstract We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers (m,a)$(m,a)$ such that m$m$ is odd, there exists n⩽m2+o(1)$n\leqslant m^{2+o(1)}$ such that φ(n)≡a(modm)$\varphi (n)\equiv a\ (\mathrm{mod}\ m)$.
Abhishek Jha
wiley   +1 more source

On Arithmetic Series involving the fractional part function

, 2020
We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the Von Mangoldt function is presented, as well as a criteria for the Riemann ...
Patkowski, Alexander E.
core