Kummer sum information

Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who...

calculate certain zeta functions. Quadratic Gauss sum Elliptic Gauss sum Jacobi sum Kummer sum Kloosterman sum Gaussian period Hasse–Davenport relation Chowla–Mordell...

of binomial coefficients Kummer's function Kummer sum Kummer variety Kummer–Vandiver conjecture Kummer's transformation of series Ideal number Regular...

2 and an odd prime number p, and for k ≥ 4 and p = 2. Gauss sum Gaussian period Kummer sum Landsberg–Schaar relation M. Murty, S. Pathak, The Mathematics...

hypergeometric functions: Kummer's (confluent hypergeometric) function M(a, b, z), introduced by Kummer (1837), is a solution to Kummer's differential equation...

sum _{j=1}^{K}\prod _{k=1}^{j}\ln _{(K-k+1)}(n)-1+o(1).} Hence, ρ Kummer = ρ Extended Bertrand − 1. {\displaystyle \rho _{\text{Kummer}}=\rho _{\text{Extended...

In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of nth roots...

exponential sums in analytical number theory. In 1978, together with Roger Heath-Brown, he disproved the Kummer conjecture on cubic Gauss sums. He proposed...

Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857)...

{x^{i}}{i!}},\end{aligned}}} which is a finite sum if b-d is a non-negative integer. Kummer's relation is 2 F 1 ( 2 a , 2 b ; a + b + 1 2 ; x ) =...

multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from...

number Genocchi number Kummer's congruences Poly-Bernoulli number Hurwitz zeta function Euler summation Stirling polynomial Sums of powers Translation...

electronic computers. For instance, Beiler writes that number theorist Ernst Kummer loved his ideal numbers, closely related to the primes, "because they had...

convergence or divergence of an infinite series ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} . If the limit of the summand is undefined or nonzero...

theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes...

Ernst Eduard Kummer studied cyclic extensions of fields as part of his work on Fermat's Last Theorem. This led to the subject now known as Kummer theory. Let...

y . {\displaystyle \sum _{n=0}^{\infty }\sum _{k=0}^{\infty }{n+k \choose k}{\frac {x^{k}y^{n}}{(n+k)!}}=e^{x+y}.} In 1852, Kummer proved that if m and...

\operatorname {Cl} _{2}(\theta )={\mathcal {L}}s_{2}^{0}(\theta )} Ernst Kummer and Rogers give the relation Li 2 ⁡ ( e i θ ) = ζ ( 2 ) − θ ( 2 π − θ )...

{\displaystyle \gamma (s,z)=\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{k!}}{\frac {z^{s+k}}{s+k}}={\frac {z^{s}}{s}}M(s,s+1,-z),} where M is Kummer's confluent hypergeometric...