Plus/minus p-adic L-functions for Hilbert modular forms

AbstractR. Pollack constructed in Pollack (2003) [13] plus/minus p-adic L-functions for elliptic modular forms, which are p-adically bounded, when the Hecke eigenvalues at p are zero (the most supersingular case). The goal of this work is to generalize his construction to Hilbert modular forms. We find a suitable condition for Hilbert modular forms corresponding to the vanishing of p-th Hecke eigenvalue in elliptic modular form case, which guarantees the existence of plus/minus p-adic L-functions which are p-adically bounded. As an application, we construct cyclotomic plus/minus p-adic L-functions for modular elliptic curves over a totally real field F under the assumption that ap(E)=0 for each prime p dividing p. We formulate a cyclotomic plus/minus Iwasawa main conjecture for such elliptic curves

Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers

Modular Symbols with Values in Beilinson-Kato Distributions

For each integer $n\geq 1$, we construct a $\operatorname{GL}_n(\mathbb Q)$-invariant modular symbol $\bm\xi_n$ with coefficients in a space of distributions that takes values in the Milnor $K_n$-group of the modular function field. The Siegel distribution $\bm\mu$ on $\mathbb Q^2$, with values in the modular function field, serves as the building block for $\bm\xi_n$; we define $\bm\xi_n$ essentially by taking the $n$-Steinberg product of $\bm\mu$. The most non-trivial part of this construction is the cocycle property of $\bm\xi_n$; we prove it by using an induction on $n$ based on the first two cases $\bm\xi_1$ and $\bm\xi_2$; the first case is trivial, and the second case essentially follows from the fact that Beilinson-Kato elements in the Milnor $K_2$-group modulo torsion satisfy the Manin relations.Comment: 20 page

Extension of Zero Voltage Switching Capability for CLLC Resonant Converter

TheCLLC resonant converter has been widely used to obtaina high power conversion efficiency with sinusoidal current waveforms and a soft switching capability. However, it has a limited voltage gain range according to the input voltage variation. The current-fed structure canbe one solution to extend the voltage gain range for the wide input voltage variation, butit has a limited zero voltage switching (ZVS) range. In this paper, the current-fed CLLC resonant converter with additional inductance is proposed to extend the ZVS range. The operational principle is analyzed to design the additional inductance for obtaining the extended ZVS range. The design methodology of the additional inductance is proposed to maximize the ZVS capability for the entire load range. The performance of the proposed method is verified with a 20 W prototype converter

Design Methodology of Tightly Regulated Dual-Output LLC Resonant Converter Using PFM-APWM Hybrid Control Method

A dual-output LLC resonant converter using pulse frequency modulation (PFM) and asymmetrical pulse width modulation (APWM) can achieve tight output voltage regulation, high power density, and high cost-effectiveness. However, an improper resonant tank design cannot achieve tight cross regulation of the dual-output channels at the worst-case load conditions. In addition, proper magnetizing inductance is required to achieve zero voltage switching (ZVS) of the power MOSFETs in the LLC resonant converter. In this paper, voltage gain of modulation methods and steady state operations are analyzed to implement the hybrid control method. In addition, the operation of the hybrid control algorithm is analyzed to achieve tight cross regulation performance. From this analysis, the design methodology of the resonant tank and the magnetizing inductance are proposed to compensate the output error of both outputs and to achieve ZVS over the entire load range. The cross regulation performance is verified with simulation and experimental results using a 190 W prototype converter