We provide, in a wide range of the parameters, an estimate for the mean-value over sifted integers of certain arithmetic functions with Dirichlet series analytically close to 1/ζK(s), where K is a number field and ζK its Dedekind zeta function.

We develop a new method referred to as the AR-z spectrum for detecting harmonic signals with exponential decay/growth contained in a noisy time-series by extending the auto regressive (AR) method of Chao & Gilbert. The method consists of (i) ‘blindly’ forcing one 2nd-order AR fit to the signal content in the frequency domain for any chosen frequency whether or not there is truly a signal; (…

The structure of seismic discontinuities in the mantle transition zone at depths of about 400 and 670 km provides important constraints on mantle convection as the associated mineral phase transformations are sensitive to thermal perturbations. Teleseismic P-to-S receiver functions have been widely used tomap the depths of the two discontinuities. In this study, we investigate the resolution of…

We investigate cloning and broadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained so far in finite dimension, and for the full algebra of operators on a Hilbert space. Moreover, we also weaken the assumption of complete positivity of the broadcasting (cloning) operation. It turns out that some results can be expressed in terms of modu…

In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it is actually possible to compute the crystalline cohomology of the curve, which is a lattice in the rigid cohomology. Following a method of Wach, we explain how to use this lattice to compute the (b…

We show that the Atiyah–Patodi–Singer reduced η-invariant of the twisted Dirac operator on a closed 4m − 1-dimensional spin manifold, with the twisted bundle being the Witten bundle appearing in the theory of elliptic genus, is a meromorphic modular form of weight 2m up to an integral q-series.We prove this result by combining our construction of certain modular characteristic fo…

Full waveform inversion (FWI) is a powerful tool used to quantify the elastic properties of the subsurface from seismic data. Because of very high computational cost, the technique has so far been used for either 2-D full elastic or 3-D acoustic media while the extension to 3-D elastic media to a realistic model size is still a challenging task. However, the Earth being 3-D, elastic and highly …

In this work, we analyse in detail how a large earthquake could cause stress changes on volcano plumbing systems and produce possible positive feed backs in promoting new eruptions. We develop a sensitivity analysis that considers several possible parameters, providing also new constraints on the methodological approach. The work is focus on the Mw 8.8 2010 earthquake that occurred along the Ch…

We present a strategy to thoroughly investigate the effects of prominent topography on the surface tilt due to a spherical pressure source.We use Etna’s topography as a case of study and, for different source positions, we compare the tilt fields calculated through (i) a 3-D boundary element method and (ii) analytical half-space solutions. We systematically determine (i) the source positions …

To elucidate the relationship between interplate temperatures and generation mechanisms for megathrust earthquakes and slow slip events (SSEs) in the Kanto district, central Japan, we performed numerical simulations on the thermal state. For this purpose, we newly developed a 2-D box-type thermal convection model that is able to handle the subduction of two oceanic plates: the young oceanic Phi…