We investigate several topics in multiplicative number theory on the distributions of the k-fold divisor function in arithmetic progressions, divisor sums, and gaps between zeros of L-functions. Applications of
Lecture Notes in Mathematics(共523册),这套丛书还有 《Algebraic Geometry》《Topics in the Theory of Riemann Surfaces》《Real Methods in Complex and CR Geometry (Lecture Notes in Mathematics, Volume 1848)》《Compactifying Moduli Spaces for Abelian Varieties》《Integrable Systems and Quantum Groups》等...
TopicsinAnalyticNumberTheory By RobertJ.LemkeOliver M.A.,UniversityofWisconsin-Madison,2010 Advisor:KenOno,Ph.D. Anabstractof AdissertationsubmittedtotheFacultyofthe JamesT.LaneySchoolofGraduateStudiesofEmoryUniversity inpartialfulfillmentoftherequirementsforthedegreeof ...
We want N(r)<N(b) , that is equivalent to N(a−bq)=N(ab−q)N(b)<N(b) since norm is multiplicative. Therefore we need to find q such that N(ab−q)<1 . Note that ab is in Q(−1,−1) over rationals Q . Therefore we may write it as (x,y,z,w) .Write q=...
Hence a stochastic multiplicative uncertainty model uses state-dependent Gaussian white noise to represent parameter uncertainty by defining a measure of ignorance, in terms of an information-theoretic entropy, and then determining the probability distribution which maximizes this measure subject to agreement...
Let R be a commutative ring, S ⊂ R a multiplicative monoid and a≠R an ideal disjoint from S. Then, there exists an ideal m that is maximal among the ideals that contain a and are disjoint from S and m is a prime ideal. (II) Prime spectrum of a ring. Definition 2.29 A proper...
This chapter presents a selection of different topics. We discuss forecasting under model uncertainty, deep quantile regression, deep composite regression and the LocalGLMnet which is an interpretable FN network architecture. Moreover, we provide a boots
VariableDescription $p$ A large prime number $g$ A generator of the multiplicative group of integers modulo $p$ $h$ The public key $x$ The private keyThe public key is $(p, g, h)$ and the private key is $(p, g, x)$.
1)Modular arithmetic– This technique is used throughout Number Theory. For example, Mod 3 means the remainder when dividing by 3. 2)Goldbach’s conjecture:“Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics. ...
where are arbitrary positive real numbers, and the here indicates that we are willing to lose an unspecified (multiplicative) constant in the estimates. I have wished in the past (e.g., in this MathOverflow answer) for a tool that could automatically determine whether such an estimate was tru...