Journal of Algebra, ISSN 0021-8693, 04/2015, Volume 428, pp. 357 - 402

In this paper, we introduce the notion of the pivotal cover Cpiv of a left rigid monoidal category C to develop a theoretical foundation for the theory of...

Frobenius–Schur indicators | Pivotal monoidal category | Rigid monoidal category | Hopf algebras | Frobenius-Schur indicators | TRACE | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | HOPF

Frobenius–Schur indicators | Pivotal monoidal category | Rigid monoidal category | Hopf algebras | Frobenius-Schur indicators | TRACE | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | HOPF

Journal Article

Journal of Algebraic Geometry, ISSN 1056-3911, 2018, Volume 27, Issue 1, pp. 1 - 20

The goal of this note is to give a short geometric proof of a theorem of Hrushovski asserting that an intersection of a correspondence with a graph of a...

MATHEMATICS | VERDIER TRACE FORMULA

MATHEMATICS | VERDIER TRACE FORMULA

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 10/2018, Volume 86, Issue 10, pp. 2247 - 2254

Let $$\texttt {R}$$ R be a finite commutative Frobenius ring and $$\texttt {S}$$ S a Galois extension of $$\texttt {R}$$ R of degree m. For positive integers k...

Information and Communication, Circuits | Chinese remainder theorem | Data Encryption | Trace map | 16P70 | Mathematics | 15A03 | 13B05 | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Finite commutative Frobenius ring | 94B05 | Coding and Information Theory | Galois extension | Combinatorics | Module | MATHEMATICS, APPLIED | CODES | COMPUTER SCIENCE, THEORY & METHODS

Information and Communication, Circuits | Chinese remainder theorem | Data Encryption | Trace map | 16P70 | Mathematics | 15A03 | 13B05 | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Finite commutative Frobenius ring | 94B05 | Coding and Information Theory | Galois extension | Combinatorics | Module | MATHEMATICS, APPLIED | CODES | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2016, Volume 159, pp. 402 - 425

We establish a relation between minimal value set polynomials defined over Fq and certain q-Frobenius nonclassical curves. The connection leads to a...

Frobenius nonclassical curve | Finite field | Minimal value set polynomial | POLYNOMIALS | TRACE | MATHEMATICS | GENERALIZED HERMITIAN CODES | FINITE-FIELDS | NORM | PLANE-CURVES

Frobenius nonclassical curve | Finite field | Minimal value set polynomial | POLYNOMIALS | TRACE | MATHEMATICS | GENERALIZED HERMITIAN CODES | FINITE-FIELDS | NORM | PLANE-CURVES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2013, Volume 219, Issue 17, pp. 9363 - 9371

Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context,...

Trace | Singular values | Approximate inverses | Frobenius norm minimization | Normal equations | Spectrum | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | PRECONDITIONERS

Trace | Singular values | Approximate inverses | Frobenius norm minimization | Normal equations | Spectrum | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | PRECONDITIONERS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 09/2019, Volume 15, Issue 8, pp. 1675 - 1691

We investigate statistics of trace of high powers of the Frobenius class for biquadratic function fields over finite fields, which generalizes the result of...

MATHEMATICS | Frobenius | trace | genus | Biquadratic curve

MATHEMATICS | Frobenius | trace | genus | Biquadratic curve

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2014, Volume 140, pp. 181 - 195

In [12], McCarthy defined a function Gnn[⋯] using the Teichmüller character of finite fields and quotients of the p-adic gamma function, and expressed the...

Characters of finite fields | Teichmüller character | p-Adic gamma function | Elliptic curves | Trace of Frobenius | Gauss sums | P-Adic gamma function | Teichmuller character | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

Characters of finite fields | Teichmüller character | p-Adic gamma function | Elliptic curves | Trace of Frobenius | Gauss sums | P-Adic gamma function | Teichmuller character | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 02/2017, Volume 65, Issue 2, pp. 351 - 360

In this paper we investigate the structure of maps on classes of Hilbert space operators leaving the determinant of linear combinations invariant. Our main...

trace class operators | Secondary 47B10 | positive definite and positive semidefinite matrices | Frobenius theorem | preserver problems | Primary 47B49 | Fredholm determinant | MATHEMATICS | ALGEBRAS | OPERATORS | TRANSFORMATIONS | Hilbert space | Operators (mathematics) | Theorems | Transformations (mathematics) | Matrices (mathematics) | Mathematical analysis | Determinants | Invariants

trace class operators | Secondary 47B10 | positive definite and positive semidefinite matrices | Frobenius theorem | preserver problems | Primary 47B49 | Fredholm determinant | MATHEMATICS | ALGEBRAS | OPERATORS | TRANSFORMATIONS | Hilbert space | Operators (mathematics) | Theorems | Transformations (mathematics) | Matrices (mathematics) | Mathematical analysis | Determinants | Invariants

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2013, Volume 261, Issue 1, pp. 219 - 236

We define a function in terms of quotients of the p-adic gamma function which generalizes earlier work of the author on extending hypergeometric functions over...

Hypergeometric functions | Elliptic curves | Modular forms | P-adic gamma function | Trace of Frobenius | trace of Frobenius | MATHEMATICS | hypergeometric functions | GAUSSIAN HYPERGEOMETRIC-SERIES | modular forms | FINITE-FIELDS | p-adic gamma function | elliptic curves

Hypergeometric functions | Elliptic curves | Modular forms | P-adic gamma function | Trace of Frobenius | trace of Frobenius | MATHEMATICS | hypergeometric functions | GAUSSIAN HYPERGEOMETRIC-SERIES | modular forms | FINITE-FIELDS | p-adic gamma function | elliptic curves

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2018, Volume 188, pp. 263 - 280

For an elliptic curve E/Q, Hasse's theorem asserts that #E(Fp)=p+1−ap, where |ap|≤2p. Assuming that E has complex multiplication, we establish asymptotics for...

Elliptic trailing prime | Frobenius distributions | Elliptic champion prime | Trace of Frobenius | Complex multiplication | Lang–Trotter conjecture | Sato–Tate conjecture | Elliptic curve | MATHEMATICS | ZETA-FUNCTION | Sato-Tate conjecture | Lang-Trotter conjecture | PRIME-NUMBERS | KIND

Elliptic trailing prime | Frobenius distributions | Elliptic champion prime | Trace of Frobenius | Complex multiplication | Lang–Trotter conjecture | Sato–Tate conjecture | Elliptic curve | MATHEMATICS | ZETA-FUNCTION | Sato-Tate conjecture | Lang-Trotter conjecture | PRIME-NUMBERS | KIND

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2001, Volume 244, Issue 1, pp. 312 - 342

We study a symmetric Markov extension of k-algebras N↪M, a certain kind of Frobenius extension with conditional expectation that is tracial on the centralizer...

Frobenius extension | Jones tower | trace | symmetric Markov extension | conditional expectation | weak Hopf algebra | endomorphism ring | basic construction | actions | Trace | Conditional expectation | Weak | Actions | Symmetric Markov extension | Hopf algebra | Endomorphism ring | Basic construction | MATHEMATICS | SUBFACTORS | INDEX

Frobenius extension | Jones tower | trace | symmetric Markov extension | conditional expectation | weak Hopf algebra | endomorphism ring | basic construction | actions | Trace | Conditional expectation | Weak | Actions | Symmetric Markov extension | Hopf algebra | Endomorphism ring | Basic construction | MATHEMATICS | SUBFACTORS | INDEX

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2016, Volume 164, pp. 282 - 298

For an elliptic curve E/Q, we define an extremal prime for E to be a prime p of good reduction such that the trace of Frobenius of E at p is ±⌊2p⌋, i.e.,...

Distribution of primes | Frobenius distributions | Elliptic curves | Trace of Frobenius | Lang–Trotter conjecture | Lang-Trotter conjecture | MATHEMATICS | L-ADIC LIFTS | AUTOMORPHY

Distribution of primes | Frobenius distributions | Elliptic curves | Trace of Frobenius | Lang–Trotter conjecture | Lang-Trotter conjecture | MATHEMATICS | L-ADIC LIFTS | AUTOMORPHY

Journal Article

Contemporary Mathematics, ISSN 0271-4132, 2017, Volume 688, pp. 125 - 137

Conference Proceeding

Linear Algebra and Its Applications, ISSN 0024-3795, 06/2013, Volume 438, Issue 11, pp. 4359 - 4362

We demonstrate some upper bounds for the spread of a matrix.

Spread | Variance | Frobenius norm | EIGENVALUES | MATHEMATICS, APPLIED | INEQUALITIES | TRACES

Spread | Variance | Frobenius norm | EIGENVALUES | MATHEMATICS, APPLIED | INEQUALITIES | TRACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2016, Volume 144, Issue 4, pp. 1493 - 1508

We prove hypergeometric type identities for a function defined in terms of quotients of the p hypergeometric series and the Fourier coefficients of a certain...

TRACE | MATHEMATICS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | SERIES | FINITE-FIELDS | HECKE OPERATORS | FROBENIUS

TRACE | MATHEMATICS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | SERIES | FINITE-FIELDS | HECKE OPERATORS | FROBENIUS

Journal Article

Eastern-European Journal of Enterprise Technologies, ISSN 1729-3774, 2017, Volume 2, Issue 9-86, pp. 11 - 21

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 05/2014, Volume 448, pp. 245 - 263

Two measures of separation between two subspaces of a finite dimensional complex vector space are introduced and investigated. The measures were inspired by...

Trace | Partitioned matrix | Commutativity of projectors | Angle and minimal angle between subspaces | Orthogonal projector | Orthogonally incident subspaces | MATHEMATICS, APPLIED | ORTHOGONAL PROJECTORS | ANGLES | COMPLEX VECTOR-SPACES | Projectors

Trace | Partitioned matrix | Commutativity of projectors | Angle and minimal angle between subspaces | Orthogonal projector | Orthogonally incident subspaces | MATHEMATICS, APPLIED | ORTHOGONAL PROJECTORS | ANGLES | COMPLEX VECTOR-SPACES | Projectors

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2018, Volume 295, Issue 2, pp. 271 - 289

We prove two transformations for the p-adic hypergeometric series which can be described as p-adic analogues of a Kummer's linear transformation and a...

P-adic gamma function | Character sum | Hypergeometric series | TRACE | MATHEMATICS | ELLIPTIC-CURVES | hypergeometric series | FINITE-FIELDS | p-adic gamma function | SPECIAL VALUES | character sum | FROBENIUS

P-adic gamma function | Character sum | Hypergeometric series | TRACE | MATHEMATICS | ELLIPTIC-CURVES | hypergeometric series | FINITE-FIELDS | p-adic gamma function | SPECIAL VALUES | character sum | FROBENIUS

Journal Article

Electronic Journal of Linear Algebra, ISSN 1537-9582, 12/2014, Volume 27, pp. 892 - 906

Let A be an n x n complex matrix with n >= 3. It is shown that at least n - 2 of the eigenvalues of A lie in the disk vertical bar z - tr A/n vertical bar <=...

Trace | Eigenvalue | Spread | Normal matrix | Localization | Frobenius norm | MATHEMATICS

Trace | Eigenvalue | Spread | Normal matrix | Localization | Frobenius norm | MATHEMATICS

Journal Article

Communications in Mathematical Sciences, ISSN 1539-6746, 2015, Volume 13, Issue 4, pp. 1033 - 1049

Phase retrieval aims to recover a signal x is an element of C-n from its amplitude measurements vertical bar|< x,a(i)>vertical bar(2), i = 1,2,..., m, where...

Difference of convex functions algorithm | Phase lift regularized by trace minus frobenius norms | Phase retrieval | Equivalent minimization problems | Karush-kuhn-tucker conditions | Convergence | MATHEMATICS, APPLIED | phase lift regularized by trace minus Frobenius norms | difference of convex functions algorithm | Karush-Kuhn-Tucker conditions | MINIMIZATION | convergence | RECONSTRUCTION | ALGORITHM | equivalent minimization problems

Difference of convex functions algorithm | Phase lift regularized by trace minus frobenius norms | Phase retrieval | Equivalent minimization problems | Karush-kuhn-tucker conditions | Convergence | MATHEMATICS, APPLIED | phase lift regularized by trace minus Frobenius norms | difference of convex functions algorithm | Karush-Kuhn-Tucker conditions | MINIMIZATION | convergence | RECONSTRUCTION | ALGORITHM | equivalent minimization problems

Journal Article

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