T-adic exponential sums under diagonal base change

Twistec T-adic exponential sums are studied. As an application, the behavior of the L-function under diagonal base chang is explicitely given

Gold type codes of higher relative dimension

Some new Gold type codes of higher relative dimension are introduced. Their weight distribution is determined

Sublattices of finite index

Assuming the Gowers Inverse conjecture and the M\"{o}bius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's theorem on Dickson's conjecture, and prove that, if $L$ is the range of a linear map of complexity $s$, and $L_1$ is a sublattice of $L$ of finite index, then $L_1$ is the range of a linear map of complexity $s$.Comment: Revised on Jan. 5, 200

The prime ideals in every class contain arbitrary large truncated classes

We prove that the prime ideals in every class of a number field contain arbitrary large truncated ideal classes.Comment: This is a generalization of Green-Tao's prime arithmetic progression theorem to number field

A sup-Hodge bound for exponential sums

The $C$-function of $T$-adic exponential sums is studeid. An explicit arithmetic bound is established for the Newton polygon of the $C$-function. This polygon lies above the Hodge polygon. It gives a sup-Hodge bound of the $C$-function of $p$-power order exponential sums

Review of D Semi-leptonic Decays

Semi-leptonic D decays continue to play an important role in the field of flavor physics. During this presentation, recent measurements from pseudo-scalar to pseudo-scalar modes, pseudo-scalar to vector modes, and rare modes will be discussed. These results are important for many purposes, such as validating the machinery of lattice QCD, extracting CKM matrix elements, and searching for new physics and new interactions.Comment: to appear in the proceedings of The 5th International Workshop on Charm Physics (Charm 2012

Generic exponential sums associated to Laurent polynomials in one variable

Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined

Arithmetic progressions of primes in short intervals

Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any given length

Subadditive stake systems

Stake systems which issue stakes as well as coins are proposed. Two subadditive stake systems are studied: one is the radical stake system, the other is the logarithmic stake system. Securities of both systems are analysed.Comment: arXiv admin note: substantial text overlap with arXiv:1804.1113

The L-functions of twisted Witt extensions

The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing the Stickelberger theorem.Comment: 16 page