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Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...

There are three types of boundary conditions commonly encountered in the solution of partial differential equations: 1. Dirichlet boundary conditions specify the value of the ...

Define a Bouniakowsky polynomial as an irreducible polynomial f(x) with integer coefficients, degree >1, and GCD(f(1),f(2),...)=1. The Bouniakowsky conjecture states that ...

There are a number of functions in mathematics commonly denoted with a Greek letter lambda. Examples of one-variable functions denoted lambda(n) with a lower case lambda ...

The cubefree part is that part of a positive integer left after all cubic factors are divided out. For example, the cubefree part of 24=2^3·3 is 3. For n=1, 2, ..., the first ...

Let phi(n) be any function, say analytic or integrable. Then int_0^inftyx^(s-1)sum_(k=0)^infty(-1)^kx^kphi(k)dx=(piphi(-s))/(sin(spi)) (1) and ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...