Modular hyperbolas
IE Shparlinski - Japanese Journal of Mathematics, 2012 - Springer
We give a survey of a variety of recent results about the distribution and some geometric
properties of points (x, y) on modular hyperbolas xy ≡ a\;(\mod m). We also outline a very …
properties of points (x, y) on modular hyperbolas xy ≡ a\;(\mod m). We also outline a very …
Effective equidistribution of primitive rational points on expanding horospheres
We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira on the
asymptotic distribution of primitive rational points on expanding closed horospheres in the …
asymptotic distribution of primitive rational points on expanding closed horospheres in the …
Statistics of ranks, determinants and characteristic polynomials of rational matrices
We consider the set of m× n matrices with rational entries having numerator and
denominator of size at most H and obtain various upper bounds on the number of such …
denominator of size at most H and obtain various upper bounds on the number of such …
On some matrix counting problems
A Mohammadi, A Ostafe… - Journal of the London …, 2024 - Wiley Online Library
On some matrix counting problems - Mohammadi - 2024 - Journal of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …
On the solvability of bilinear equations in finite fields
IE Shparlinski - Glasgow Mathematical Journal, 2008 - cambridge.org
We consider the equation over a finite field q of q elements, with variables from arbitrary
sets. The question of solvability of such and more general equations has recently been …
sets. The question of solvability of such and more general equations has recently been …
Some counting questions for matrix products
M Afifurrahman - Bulletin of the Australian Mathematical Society, 2024 - cambridge.org
SOME COUNTING QUESTIONS FOR MATRIX PRODUCTS Page 1 Bull. Aust. Math. Soc. 110
(2024), 32–43 doi:10.1017/S0004972723001004 SOME COUNTING QUESTIONS FOR …
(2024), 32–43 doi:10.1017/S0004972723001004 SOME COUNTING QUESTIONS FOR …
Distribution of modular inverses and multiples of small integers and the sato-tate conjecture on average
IE Shparlinski - Michigan Mathematical Journal, 2008 - projecteuclid.org
A rather old conjecture asserts that if m= p is prime then, for any fixed ε> 0 and sufficiently
large p, for every integer a there are integers x and y with| x|,| y|≤ p1/2+ ε and such that a≡ …
large p, for every integer a there are integers x and y with| x|,| y|≤ p1/2+ ε and such that a≡ …
Distribution of determinant of matrices with restricted entries over finite fields
LA Vinh - arXiv preprint arXiv:0903.2508, 2009 - arxiv.org
For a prime power $ q $, we study the distribution of determinent of matrices with restricted
entries over a finite field $\mathbbm {F} _q $ of $ q $ elements. More precisely, let $ N_d …
entries over a finite field $\mathbbm {F} _q $ of $ q $ elements. More precisely, let $ N_d …
Some applications of representation theory to the sum-product phenomenon
ID Shkredov - arXiv preprint arXiv:2307.03156, 2023 - arxiv.org
arXiv:2307.03156v1 [math.NT] 6 Jul 2023 Page 1 arXiv:2307.03156v1 [math.NT] 6 Jul 2023
Some applications of representation theory to the sum–product phenomenon ID Shkredov …
Some applications of representation theory to the sum–product phenomenon ID Shkredov …
On the determinants and permanents of matrices with restricted entries over prime fields
Let A be a set in a prime field F p. We prove that d× d matrices with entries in A determine
almost| A| 3+ 1 4 5 distinct determinants and almost| A| 2− 1 6 distinct permanents when| A …
almost| A| 3+ 1 4 5 distinct determinants and almost| A| 2− 1 6 distinct permanents when| A …