Products related to Adic:
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p-adic Numbers, p-adic Analysis, and Zeta-Functions
Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu.I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle.He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and GTM 97: "Introduction to Elliptic Curves and Modular Forms (Springer-Verlag).
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p-adic Differential Equations
Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations.Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations.The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties.This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.
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p-adic Banach Space Representations : With Applications to Principal Series
This book systematically develops the theory of continuous representations on p-adic Banach spaces.Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series.Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations.Part 1 culminates with the duality between Banach space representations and Iwasawa modules.This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
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Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas
A groundbreaking contribution to number theory that unifies classical and modern resultsThis book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus.The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory.This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower.Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters.He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology.This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation.Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators.Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified.These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
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What is the b-adic representation?
The b-adic representation is a way of representing a non-negative integer using a base b. It involves expressing the integer as a sum of multiples of powers of b. For example, in base 10, the number 365 can be represented as 3*10^2 + 6*10^1 + 5*10^0. This representation allows for easy conversion between different bases and is commonly used in computer science and number theory.
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How do you multiply 7-adic numbers?
To multiply 7-adic numbers, you can use the same method as multiplying regular integers, but with carrying out the operations modulo 7 at each step. Start by multiplying the corresponding digits of the two numbers, then carry over any excess to the next digit. Repeat this process for each digit position. Remember that in the 7-adic number system, each digit can only be between 0 and 6.
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What is the definition of a b-adic fraction?
A b-adic fraction is a way of representing a real number using a base b expansion. It is similar to a decimal expansion, but instead of using base 10, it uses base b. The b-adic expansion of a number consists of a sequence of digits, each of which represents a multiple of a power of b. The expansion can be finite or infinite, and it can be used to represent both rational and irrational numbers.
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How do you convert recurring fractions into q-adic representation?
To convert recurring fractions into q-adic representation, we can use the formula for converting a recurring fraction to a q-adic number. First, we express the recurring fraction as a continued fraction. Then, we use the formula for converting a continued fraction to a q-adic number, which involves finding the convergents of the continued fraction and expressing them in terms of powers of q. This process allows us to represent the recurring fraction as a q-adic number.
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The Eigenbook : Eigenvarieties, families of Galois representations, p-adic L-functions
?This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them.These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research.For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
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Tiny Living Spaces : Innovative Design Solutions
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Designing Innovative Sustainable Neighborhoods
This book covers fundamental aspects of neighborhood planning and architecture along sustainable principles.Written by a designer and instructor, the book’s fully illustrated chapters provide detailed insights into contemporary strategies that architects, planners and builders are integrating into their thought processes and residential design practices. Past approaches to planning and design modes of dwellings and neighborhoods can no longer sustain new demands and require innovative thinking.This book explores new outlooks on neighborhood design, which are propelled by fundamental changes that touch upon environmental, economic and social aspects.It presents contemporary well-designed and illustrated examples of communities and detailed analysis of topics including the depletion of non-renewable natural resources, elevated levels of greenhouse gas emissions and climate change.It also explores the increasing costs of material, labor, land and infrastructure, which pose economic challenges; as well as social challenges including the need for walkable communities and the increase in live-work environments. The need to think innovatively about neighborhoods is at the core of this book, which will be useful to students and practitioners of urban design, urban planning, geography and urban systems; and to architecture studios focused on sustainable residential development.
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Collaborative Spaces at Work : Innovation, Creativity and Relations
Collaborative spaces are more than physical locations of work and production.They present strong identities centered on collaboration, exchange, sense of community, and co-creation, which are expected to create a physical and social atmosphere that facilitates positive social interaction, knowledge sharing, and information exchange.This book explores the complex experiences and social dynamics that emerge within and between collaborative spaces and how they impact, sometimes unexpectedly, on creativity and innovation. Collaborative Spaces at Work is timely and relevant: it will address the gap in critical understandings of the role and outcomes of collaborative spaces.Advancing the debate beyond regional development rhetoric, the book will investigate, through various empirical studies, if and how collaborative spaces do actually support innovation and the generation of new ideas, products, and processes. The book is intended as a primary reference in creativity and innovation, workspaces, knowledge and creative workers, and urban studies.Given its short chapters and strong empirical orientation, it will also appeal to policy makers interested in urban regeneration, sustaining innovation, and social and economic development, and to managers of both collaborative spaces and companies who want to foster creativity within larger organizations.It can also serve as a textbook in master’s degrees and PhD courses on innovation and creativity, public management, urban studies, management of work, and labor relations.
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Why is E-commerce not sustainable?
E-commerce is not sustainable for several reasons. First, the increase in online shopping leads to higher energy consumption and carbon emissions from transportation and packaging. Additionally, the rise of fast fashion and disposable consumer goods in e-commerce contributes to environmental degradation and waste. Furthermore, the reliance on large warehouses and fulfillment centers for e-commerce operations can lead to land use and habitat destruction. Finally, the convenience of e-commerce can lead to overconsumption and unnecessary purchases, further straining the environment.
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Are books or e-books more sustainable?
Books are generally considered more sustainable than e-books. While e-books do not require physical materials like paper and ink, they have a significant environmental impact due to the energy and resources required to produce and dispose of electronic devices. Additionally, the production and disposal of e-readers contribute to electronic waste, which can be harmful to the environment. On the other hand, books can be made from sustainably sourced materials and are often recyclable. Therefore, in terms of sustainability, books are generally the more environmentally friendly option.
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What are E-Tech weapons in Borderlands 2?
E-Tech weapons in Borderlands 2 are a special type of weapon that feature unique effects and abilities. These weapons are characterized by their glowing purple color and are considered rare and powerful. E-Tech weapons use a special type of elemental damage that can be particularly effective against certain enemy types. Players can find E-Tech weapons as drops from enemies or in chests throughout the game world.
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What are some ideas for an innovative and sustainable product that does not exist yet?
One innovative and sustainable product idea could be a biodegradable and compostable alternative to single-use plastic packaging, such as a food wrap or container made from plant-based materials. Another idea could be a solar-powered water purification system that can provide clean drinking water in remote or disaster-stricken areas. Additionally, a wearable technology that uses kinetic energy from movement to generate electricity for charging electronic devices could be a sustainable and innovative product.
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