Topics in analytic and combinatorial number theory by Walker, A

Mathematical gems : from elementary combinatories, number theory and geometry / by Honsberger, Ross, 1929-

Combinatorial and Additive Number Theory III : CANT, New York, USA, 2017 and 2018 / by International Conference on Combinatorial and Additive Number Theory (2017 : New York, N.Y.) 637053, Nathanson, Melvyn B. (Melvyn Bernard), 1944-, editor 465639

Subjects: “…Combinatorial number theory…”

Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function by Feng Qi, Chao-Ping Chen , Dongkyu Lim

“…In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the Catalan numbers in combinatorial number theory. …”
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A Brief Survey and an Analytic Generalization of the Catalan Numbers and Their Integral Representations by Jian Cao, Wen-Hui Li, Da-Wei Niu, Feng Qi, Jiao-Lian Zhao

“…In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy’s integral formula in the theory of complex functions, and point out potential directions for further study.…”
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On monotonicity of ranks of partitions, positivity of truncated series, and transformation formulas for theta series by Ho, Thi Phuong Nhi

“…We discuss three different topics in combinatorial number theory. In the first topic, we form several truncated series from the quintuple product identity and its specialised versions, then prove that the coeffcients of these series exhibit uniformity in sign. …”
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Counting primes, groups and manifolds by Goldfeld, D, Lubotzky, A, Nikolov, N, Pyber, L

“….$ The proof is based on the Bombieri-Vinogradov `Riemann hypothesis on the average' and on the solution of a new type of extremal problem in combinatorial number theory. Similar surprisingly sharp estimates are obtained for the subgroup growth of lattices in higher rank semisimple Lie groups. …”

Top Coefficients of the Denumerant by Velleda Baldoni, Nicole Berline, Brandon Dutra, Matthias Köppe, Michele Vergne, Jesus De Loera

“…It is well-known that $E(\alpha)(t)$ is a quasipolynomial function of $t$ of degree $N$. In combinatorial number theory this function is known as the $\textit{denumerant}$. …”
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