this continuation observes that the series for the zeta function and the Dirichlet eta function satisfy the relation ( 1 − 2 2 s ) ζ ( s ) = η ( s ) = ∑...

associate Prof. in Goettingen). Received doctorate 1856 under Dirichlet; Thesis: "Ueber die Funktion π von Gauss mit complexem Argument".. Baez, John (November...

automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a...

Many generalizations of the Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function...

one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function...

techniques. Walsh, J. L. (1928). "Über die Entwicklung einer harmonischen Funktion nach harmonischen Polynomen". J. Reine Angew. Math. 159: 197–209. Walsh...

of harmonic functions that arises from the solution of the classical Dirichlet problem. In probability theory, the harmonic measure of a subset of the...

m(n)>1.826054.} The connection to the Riemann hypothesis is based on the Dirichlet series for the reciprocal of the Riemann zeta function, 1 ζ ( s ) = ∑...

zeta function, and the product is taken over primes. Then, using this Dirichlet series with Perron's formula, one obtains 1 2 π i ∫ c − i ∞ c + i ∞ x...

(1918–1919), "Über die Beziehung zwischen Anwachsen und Nullstellen der Zeta-Funktion", Ofversigt Finska Vetensk. Soc., 61 (9) Bourgain, Jean (2017), "Decoupling...

Friedrich-Wilhelms-University, where he was taught by Peter Gustav Lejeune Dirichlet and Jakob Steiner. In 1854 he received his doctorate in Richelot in Königsberg...

vol. 2. Partielle Differentialgleichungen 1er Ordnung für eine gesuchte Funktion, Akad. Verlagsgesell. Rozov, N. Kh. (2001) [1994], "Clairaut equation"...

"Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Funktion mit numerischen Coeffizienten einer endlichen Anzahl solcher Formen ist"...

Integral, CRC Press, ISBN 978-1-4665-8807-3 Rychlík, Karel (1923), Über eine Funktion aus Bolzanos handschriftlichem Nachlasse Schwartzman, Steven (1994), The...