A Short Note on Discrete Log Problem in $F_p$

关于混合特征完备离散赋值域同构类型的一个注记

A note on isomorphism types of complete discretely valued fields of mixed characteristic

本文确定了混合特征完备离散赋值域由其截断赋值环同构类决定所需的最小截断水平。

A note on the p-adic log-gamma functions

In this paper we prove that q-Euler numbers are occured in the coefficients of some stirling type seies for p-adic analytic q-log gamma function

A note on log-algebraicity on elliptic curves

We analyze log-algebraic power series identities for formal groups of elliptic curves over $\mathbb{Q}$ which arise from modular parametrizations. We further investigate applications to special values of elliptic curve $L$-functions.

Notes on $\log(ζ(s))^{\prime\prime}$

Motivated by the connection to the pair correlation of the Riemann zeros, we investigate the second derivative of the logarithm of the Riemann zeta function, in particular the zeros of this function. Theorem 1 gives a zero-free region. Theorem 2 gives an asymptotic estimate for the number of nontrivial zeros to height T. Theorem 3 is a zero density estimate.

A note on logarithmic growth Newton polygons of $p$-adic differential equations

In this paper, we answer a question due to Y. André related to B. Dwork's conjecture on a specialization of the logarithmic growth of solutions of $p$-adic linear differential equations. Precisely speaking, we explicitly construct a $\nabla$-module $M$ over $\mathbb{Q}_p[[X]]_0$ of rank 2 such that the left endpoint of the special log-growth Newton polygon of $M$ is strictly above the left endpoint of the generic log-growth Newton polygon of $M$.

A note on Carmichael numbers in residue classes

Improving on some recent results of Matomäki and of Wright, we show that the number of Carmichael numbers to $X$ in a coprime residue class exceeds $X^{1/(6\log\log\log X)}$ for all sufficiently large $X$ depending on the modulus of the residue class.