2014, CRM monograph series, ISBN 9781470419127, Volume 35., v, 152

Number theory -- Discontinuous groups and automorphic forms -- Theta series; Weil representation; theta correspondences | Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Arithmetic aspects of modular and Shimura varieties | Number theory -- Discontinuous groups and automorphic forms -- Relations with algebraic geometry and topology | Arithmetical algebraic geometry | Shimura varieties | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Modular and Shimura varieties

Book

Journal of the American Mathematical Society, ISSN 0894-0347, 10/2014, Volume 27, Issue 4, pp. 1043 - 1115

-modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually...

Morphisms | Integers | Commutativity | Homomorphisms | Triangulation | Mathematical theorems | Algebra | Mathematical rings | Mathematical duality | Arithmetic | MATHEMATICS | GL(Q(P)) | FIELDS | P-ADIC REPRESENTATIONS | FINITENESS | SELMER GROUPS | TRIANGULINE REPRESENTATIONS | RHAM REPRESENTATIONS | OVERCONVERGENT MODULAR-FORMS

Morphisms | Integers | Commutativity | Homomorphisms | Triangulation | Mathematical theorems | Algebra | Mathematical rings | Mathematical duality | Arithmetic | MATHEMATICS | GL(Q(P)) | FIELDS | P-ADIC REPRESENTATIONS | FINITENESS | SELMER GROUPS | TRIANGULINE REPRESENTATIONS | RHAM REPRESENTATIONS | OVERCONVERGENT MODULAR-FORMS

Journal Article

ACM Transactions on Mathematical Software, ISSN 0098-3500, 08/2016, Volume 43, Issue 1, p. 5

Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes...

Integer product | Matrix product | Modular integer arithmetic | Mathemagix | Polynomial product | Fast Fourier transform | COMPUTER SCIENCE, SOFTWARE ENGINEERING | matrix product | MATHEMATICS, APPLIED | integer product | ALGORITHMS | fast Fourier transform | DIVISION | polynomial product | Algorithms | Research | Mathematical research | Arithmetic

Integer product | Matrix product | Modular integer arithmetic | Mathemagix | Polynomial product | Fast Fourier transform | COMPUTER SCIENCE, SOFTWARE ENGINEERING | matrix product | MATHEMATICS, APPLIED | integer product | ALGORITHMS | fast Fourier transform | DIVISION | polynomial product | Algorithms | Research | Mathematical research | Arithmetic

Journal Article

1964, [1st ed.]. --, School mathematics series, vi, 91 p. illus.

Book

ACM Transactions on Programming Languages and Systems (TOPLAS), ISSN 1558-4593, 08/2007, Volume 29, Issue 5, pp. 29 - es

We consider integer arithmetic modulo a power of 2 as providedby mainstream programming languages like Java or standardimplementations of C...

interprocedural analysis | modular arithmetic | Program analysis | abstract interpretation | affine relation | Abstract interpretation | Affine relation | Interprocedural analysis | Modular arithmetic | COMPUTER SCIENCE, SOFTWARE ENGINEERING | algorithms | program analysis | theory | verification | Usage | Algorithms | Methods | Programming languages

interprocedural analysis | modular arithmetic | Program analysis | abstract interpretation | affine relation | Abstract interpretation | Affine relation | Interprocedural analysis | Modular arithmetic | COMPUTER SCIENCE, SOFTWARE ENGINEERING | algorithms | program analysis | theory | verification | Usage | Algorithms | Methods | Programming languages

Journal Article

ACM Transactions on Programming Languages and Systems (TOPLAS), ISSN 0164-0925, 01/2015, Volume 37, Issue 1, pp. 1 - 35

...Interval Analysis and Machine Arithmetic: Why Signedness Ignorance Is Bliss GRAEME GANGE, JORGE A. NAVAS, PETER SCHACHTE, HARALD SØNDERGAARD, and PETER J...

modular arithmetic | overflow | LLVM | interval analysis | program analysis | Abstract interpretation | machine arithmetic | AUTOMATIC ABSTRACTION | Theory | Languages | Verification | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | Reliability | Modular arithmetic | Analysis | Arithmetic logic unit | Computer arithmetic and logic units | Integers | Intervals | Computation | Handles | Program verification (computers) | Strings | Programming languages | Arithmetic

modular arithmetic | overflow | LLVM | interval analysis | program analysis | Abstract interpretation | machine arithmetic | AUTOMATIC ABSTRACTION | Theory | Languages | Verification | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Algorithms | Reliability | Modular arithmetic | Analysis | Arithmetic logic unit | Computer arithmetic and logic units | Integers | Intervals | Computation | Handles | Program verification (computers) | Strings | Programming languages | Arithmetic

Journal Article

ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 08/2016, Volume 43, Issue 1, pp. 1 - 37

Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes...

Modular integer arithmetic | matrix product | Mathemagix | fast Fourier transform | integer product | polynomial product | Integers | Fourier transforms | Algorithms | Mathematical analysis | Mathematical models | Polynomials | Computer algebra | Arithmetic | Mathematical Software | Computer Science

Modular integer arithmetic | matrix product | Mathemagix | fast Fourier transform | integer product | polynomial product | Integers | Fourier transforms | Algorithms | Mathematical analysis | Mathematical models | Polynomials | Computer algebra | Arithmetic | Mathematical Software | Computer Science

Journal Article

Progress in mathematics, Volume 20, xvi, 214 p. --

Book

Duke Mathematical Journal, ISSN 0012-7094, 06/2016, Volume 165, Issue 9, pp. 1629 - 1693

Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented by a surface of "low" genus, and we give evidence...

FORMS | MATHEMATICS | ELLIPTIC-CURVES | ANALYTIC TORSION | NUMBER | REPRESENTATIONS | BOUNDS | MULTIPLICITY ONE | COEFFICIENTS | VARIETIES | SPECTRUM

FORMS | MATHEMATICS | ELLIPTIC-CURVES | ANALYTIC TORSION | NUMBER | REPRESENTATIONS | BOUNDS | MULTIPLICITY ONE | COEFFICIENTS | VARIETIES | SPECTRUM

Journal Article

Journal of Cryptographic Engineering, ISSN 2190-8508, 9/2018, Volume 8, Issue 3, pp. 211 - 226

.... Montgomery modular multiplication (MMM) integrated by the spectral arithmetic can be a suitable solution...

Number-theoretic weighted transform (NWT) | Data Structures, Cryptology and Information Theory | Montgomery modular multiplication | Number-theoretic transform (NTT) | Data Encryption | Computer Science | Fast Fourier transform (FFT) | Communications Engineering, Networks | Circuits and Systems | Computer Communication Networks | Operating Systems

Number-theoretic weighted transform (NWT) | Data Structures, Cryptology and Information Theory | Montgomery modular multiplication | Number-theoretic transform (NTT) | Data Encryption | Computer Science | Fast Fourier transform (FFT) | Communications Engineering, Networks | Circuits and Systems | Computer Communication Networks | Operating Systems

Journal Article

1982, Progress in mathematics, ISBN 3764330880, Volume 20., xvi, 214

Book

1997, ISBN 9780521582285, xiii, 280

.... It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic...

Curves, Elliptic

Curves, Elliptic

Book

2011, Student mathematical library : IAS/Park City mathematical subseries, ISBN 0821852426, Volume 58, xiv, 195

Book

14.
Full Text
Improving recovered image quality in secret image sharing by simple modular arithmetic

Signal Processing: Image Communication, ISSN 0923-5965, 08/2018, Volume 66, pp. 42 - 49

.... To obtain computational efficiency, simple modular arithmetic on a prime number is still adopted...

Polynomial | Finite field | Distortion | Secret image sharing | Modular | Visual quality | STEGANOGRAPHY | SCHEME | AUTHENTICATION | SMALLER SHADOW IMAGES | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Information science | Analysis

Polynomial | Finite field | Distortion | Secret image sharing | Modular | Visual quality | STEGANOGRAPHY | SCHEME | AUTHENTICATION | SMALLER SHADOW IMAGES | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Information science | Analysis

Journal Article

1991, Monographs and textbooks in pure and applied mathematics, ISBN 0824785266, Volume 148., xii, 216

Book

IEEE Transactions on Computers, ISSN 0018-9340, 12/2017, Volume 66, Issue 12, pp. 2019 - 2030

.... In this article, we investigate its performance in multiprecision arithmetic for number-theoretic applications...

elliptic curve method | integer factorization | Graphics processing units | Context awareness | Computer architecture | Elliptic curve cyrptography | Kalray MPPA-256 manycore processor | Noise measurement | VLIW | multiprecision modular arithmetic | Electronic countermeasures | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | MULTIPLICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Ellipse | Modular arithmetic | Graphics coprocessors | Research | Curves, Elliptic | State of the art | Microprocessors | Curves | Arithmetic | Cryptography and Security | Computer Arithmetic | Computer Science

elliptic curve method | integer factorization | Graphics processing units | Context awareness | Computer architecture | Elliptic curve cyrptography | Kalray MPPA-256 manycore processor | Noise measurement | VLIW | multiprecision modular arithmetic | Electronic countermeasures | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | MULTIPLICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Ellipse | Modular arithmetic | Graphics coprocessors | Research | Curves, Elliptic | State of the art | Microprocessors | Curves | Arithmetic | Cryptography and Security | Computer Arithmetic | Computer Science

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 5/2011, Volume 25, Issue 1, pp. 49 - 56

...). In particular, we identify an infinite family of arithmetic progressions modulo arbitrary powers of 3 such that b 13(n)≡0 (mod 3).

11P83 | Fourier Analysis | Functions of a Complex Variable | Regular partitions | Fourier coefficients of modular forms | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | MATHEMATICS | DISTINCT PARTS

11P83 | Fourier Analysis | Functions of a Complex Variable | Regular partitions | Fourier coefficients of modular forms | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | MATHEMATICS | DISTINCT PARTS

Journal Article

Russian Mathematical Surveys, ISSN 0036-0279, 04/2011, Volume 66, Issue 2, pp. 369 - 420

...Home Search Collections Journals About Contact us My IOPscience Arithmetic hypergeometric series This article has been downloaded from IOPscience. Please...

Algorithm of creative telescoping | Hypergeometric series | Zeta value | Diophantine approximation | Calabi-Yau differential equation | Mahler measure | Ramanujan's mathematics | Irrationality measure | Modular form | Wilf-Zeilberger theory | modular form | Q-ANALOG | FRACTIONAL-PARTS | zeta value | SPECIAL VALUES | LATTICE SUMS | FUCHS DIFFERENTIAL-EQUATIONS | TAYLOR COEFFICIENTS | PERMUTATION GROUP | MATHEMATICS | hypergeometric series | ZETA-FUNCTION | MAHLERS MEASURE | algorithm of creative telescoping | irrationality measure

Algorithm of creative telescoping | Hypergeometric series | Zeta value | Diophantine approximation | Calabi-Yau differential equation | Mahler measure | Ramanujan's mathematics | Irrationality measure | Modular form | Wilf-Zeilberger theory | modular form | Q-ANALOG | FRACTIONAL-PARTS | zeta value | SPECIAL VALUES | LATTICE SUMS | FUCHS DIFFERENTIAL-EQUATIONS | TAYLOR COEFFICIENTS | PERMUTATION GROUP | MATHEMATICS | hypergeometric series | ZETA-FUNCTION | MAHLERS MEASURE | algorithm of creative telescoping | irrationality measure

Journal Article

Computer Aided Chemical Engineering, ISSN 1570-7946, 2015, Volume 37, pp. 767 - 772

The ability to determine enclosures for the image set of nonlinear functions is pivotal to many applications in engineering. This paper presents a method for...

Interval Arithmetic | Function Bounding | Ellipsoids

Interval Arithmetic | Function Bounding | Ellipsoids

Conference Proceeding

20.
Full Text
Efficient arithmetic on ARM‐NEON and its application for high‐speed RSA implementation

Security and Communication Networks, ISSN 1939-0114, 12/2016, Volume 9, Issue 18, pp. 5401 - 5411

...) and a massive body of research on vector‐parallel implementations of modular arithmetic, which are crucial components for modern public...

RSA | modular arithmetic | ARM‐NEON | SIMD‐level parallelism | vector instructions | public‐key cryptography | public-key cryptography | ARM-NEON | SIMD-level parallelism | MULTIPLICATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | Platforms | Multiplication | Scanning | Algorithms | Representations | Cryptography | Digital signatures | Arithmetic

RSA | modular arithmetic | ARM‐NEON | SIMD‐level parallelism | vector instructions | public‐key cryptography | public-key cryptography | ARM-NEON | SIMD-level parallelism | MULTIPLICATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | Platforms | Multiplication | Scanning | Algorithms | Representations | Cryptography | Digital signatures | Arithmetic

Journal Article

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