Mixed motives and linear forms in the Catalan constant
Abstract We first give a geometric construction of a two‐dimensional mixed motive over Q${\mathbb {Q}}$ with the Catalan constant G=1−1/32+1/52−1/72+⋯${\mathbf {G}}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and G${\mathbf {G}}$.
Payman Eskandari +2 more
wiley +1 more source
Three methods for measuring the Earth's magnetic field intensity in Apis mellifera (Hymenoptera: Apidae) drone congregation areas. [PDF]
Pulido-Guarín H +5 more
europepmc +1 more source
Bordered Floer homology, handlebody detection, and compressing diffeomorphisms
Abstract We show that, up to connected sums with integer homology L$L$‐spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson–Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect ...
Akram Alishahi, Robert Lipshitz
wiley +1 more source
The shifted convolution problem in function fields. [PDF]
Florea A, Lalín M, Malik A, Sahay A.
europepmc +1 more source
Bounded exponential sums with multiplicative coefficients
Abstract We investigate when the exponential sum Sf(x,α):=∑n⩽xf(n)e(nα)$S_f(x,\alpha) := \sum _{n\leqslant x}f(n)\mathrm{e}(n\alpha)$ is bounded, for a multiplicative function f$f$ and α∈R$\alpha \in \mathbb {R}$. We show that under natural assumptions, Sf(x,α)$S_f(x,\alpha)$ is bounded only when f$f$ is very close to a twisted Dirichlet character χ(n ...
Péa Bazin, Ihor Pylaiev, Fred Tyrrell
wiley +1 more source
New low-genus desingularizations of three Clifford tori and related characterizations. [PDF]
Kapouleas N, Wiygul D.
europepmc +1 more source
Zeros of polynomials in derivatives of automorphic L$L$‐functions
Abstract Let Fm$\mathfrak {F}_m$ be the set of all cuspidal automorphic representations of GLm(AQ)$\mathrm{GL}_m(\mathbb {A}_{\mathbb {Q}})$, and let F(s,π)$F(s,\bm {\pi })$ be a polynomial in the derivatives of L$L$‐functions associated with representations π∈⋃m=1∞Fm$\pi \in \bigcup _{m=1}^{\infty } \mathfrak {F}_m$. We establish an asymptotic formula
Anji Dong +2 more
wiley +1 more source
Coding for channels with intermittent feedback and its security analysis. [PDF]
Yang J, Huang Q, Lin Y.
europepmc +1 more source
An effective Bombieri–Vinogradov error term for sifting problems
Abstract In number theory, many major results related to the additive properties of primes are proven using the methods of sieve theory. However, in nearly every case, the existing proofs of these results are ineffective, in that explicit values for which they hold cannot be computed.
Daniel R. Johnston
wiley +1 more source
Multi-chaotic signal identification employing a causal cross-correlation neural network. [PDF]
Wang B, Piao X, Chen C, Guo E, Zhang X.
europepmc +1 more source

