A5046095433- Advanced Algebra and Geometry
- Analytic Number Theory Research
- Algebraic Geometry and Number Theory
- Algebraic structures and combinatorial models
- Coding theory and cryptography
- Advanced Topics in Algebra
- Cooperative Communication and Network Coding
- Mathematical Dynamics and Fractals
- Error Correcting Code Techniques
- Finite Group Theory Research
- graph theory and CDMA systems
- Communism, Protests, Social Movements
- Historical Studies and Socio-cultural Analysis
- Meromorphic and Entire Functions
- Limits and Structures in Graph Theory
- Vietnamese History and Culture Studies
Alfréd Rényi Institute of Mathematics
2014-2024
Budapest University of Technology and Economics
2024
Hungarian Academy of Sciences
2016-2017
We construct a perverse sheaf related to the matrix exponential sums investigated by Erdélyi and Tóth [<italic>Matrix Kloosterman sums</italic>, 2021, arXiv:2109.00762]. As this appears as summand of certain tensor product sheaves, we can establish exact structure cohomology attached relating it Springer correspondence using recursion formula Tóth.
Abstract We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on case moduli. These exponential arise in theory horocyclic flow $$GL_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:math> .
Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>C</m:mi> </m:math> C be a linear code of length <m:mi>n</m:mi> n and dimension <m:mi>k</m:mi> k over the finite field <m:msub> <m:mrow> <m:mi mathvariant="double-struck">F</m:mi> </m:mrow> <m:msup> <m:mi>q</m:mi> <m:mi>m</m:mi> </m:msup> </m:msub> {{\mathbb{F}}}_{{q}^{m}} . The trace mathvariant="normal">Tr</m:mi> <m:mo>(</m:mo> <m:mo>)</m:mo> {\rm{Tr}}\left(C) is same subfield {{\mathbb{F}}}_{q} obvious upper bound for...
We study a family of exponential sums that arises in the expanding horospheres on GL n .We prove an explicit version general purity and find optimal bounds for these sums.
Let $K$ be a global field of finite characteristic $p\geq2$, and let $E/K$ non-isotrivial elliptic curve. We give an asympotoic formula the number places $\nu$ for which reduction $E$ at is cyclic group. Moreover we determine when Dirichlet density those 0.
We study the Schneider-Vigneras functor attaching a module over Iwasawa algebra $\Lambda(N_0)$ to $B$-representation for irreducible modulo $\pi$ principal series of group $\mathrm{GL}_n(F)$ any finite field extension $F|\mathbb{Q}_p$.
Let $C$ be a linear code of length $n$ and dimension $k$ over the finite field $\mathbb{F}_{q^m}$. The trace $\mathrm{Tr}(C)$ is same subfield $\mathbb{F}_q$. obvious upper bound for $\mathbb{F}_q$ $mk$. If equality holds, then we say that has maximum dimension. problem finding true codes their duals relevant size public key various code-based cryptographic protocols. $C_{\mathbf{a}}$ denote obtained from multiplier vector $\mathbf{a}\in (\mathbb{F}_{q^m})^n$. In this paper, give lower...
We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on case moduli. These exponential arise in theory horocyclic flow $\mathrm{GL}_n$.
We establish the exact structure of cohomology associated to a certain matrix exponential sum investigated in prior work (arXiv:2109.00762) first and last author.
We study a family of exponential sums that arises in the horocyclic flow on $\mathrm{GL}_n$. prove an explicit version general purity and find optimal bounds for these sums.