Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Class of Incomplete Character Sums
198
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Using $ell$-adic cohomology of tensor inductions of lisse $overline{mathbb Q}_ell$-sheaves, we study a class of incomplete character sums.
rate research
Read More
We deduce Katzs theorems for $(A,B)$-exponential sums over finite fields using $ell$-adic cohomology and a theorem of Denef-Loeser, removing the hypothesis that $A+B$ is relatively prime to the characteristic $p$. In some degenerate cases, the Betti number estimate is improved using toric decomposition and Adolphson-Sperbers bound for the degree of $L$-functions. Applying the facial decomposition theorem in cite{W1}, we prove that the universal family of $(A,B)$-polynomials is generically ordinary for its $L$-function when $p$ is in certain arithmetic progression.
We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)-character variety. The calculation also leads to several conjectures about the cohomology of M_n: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n = 2.
In the present article, we use Robbas method to give an estimation of the Newton polygon for the L function on torus.
We give upper bounds for the level and the Pythagoras number of function fields over fraction fields of integral Henselian excellent local rings. In particular, we show that the Pythagoras number of $mathbb{R}((x_1,dots,x_n))$ is $leq 2^{n-1}$, which answers positively a question of Choi, Dai, Lam and Reznick.
We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular form defined by a covariant we express the order of vanishing along the locus of products of elliptic curves in terms of the covariant.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
