Search Results - "The Ramanujan journal"

Log-concavity of the partition function by DeSalvo, Stephen, Pak, Igor

“…We prove that the partition function p ( n ) is log-concave for all  n > 25 . We then extend the results to resolve two related conjectures by Chen and one by…”
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Proofs of some partition identities conjectured by Kanade and Russell by Rosengren, Hjalmar

“…Kanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some of which are related to level 2 characters of the affine Lie algebra A…”
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Explicit estimates of some functions over primes by Dusart, Pierre

“…New results have been found about the Riemann hypothesis. In particular, we noticed an extension of zero-free region and a more accurate location of zeros in…”
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Inequalities and infinite product formula for Ramanujan generalized modular equation function by Wang, Miao-Kun, Li, Yong-Min, Chu, Yu-Ming

“…We present several inequalities for the Ramanujan generalized modular equation function μ a ( r ) = π F ( a , 1 - a ; 1 ; 1 - r 2 ) / [ 2 sin ( π a ) F ( a , 1…”
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On a Tauberian theorem of Ingham and Euler–Maclaurin summation by Bringmann, Kathrin, Jennings-Shaffer, Chris, Mahlburg, Karl

“…We discuss two theorems in analytic number theory and combinatory analysis that have seen increased use in recent years. A corollary to a Tauberian theorem of…”
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Precise estimates for the solution of Ramanujan’s generalized modular equation by Wang, Miao-Kun, Chu, Yu-Ming, Zhang, Wen

“…In the article, we present several monotonicity theorems and inequalities for the modular equation functions m a ( r ) and μ a ( r ) , and find the…”
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On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane by Chiang, Yik-Man, Feng, Shao-Ji

“…We investigate the growth of the Nevanlinna characteristic of f ( z + η ) for a fixed η ∈ C in this paper. In particular, we obtain a precise asymptotic…”
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Asymptotics of Nahm sums at roots of unity by Garoufalidis, Stavros, Zagier, Don

“…We give a formula for the radial asymptotics to all orders of the special q -hypergeometric series known as Nahm sums at complex roots of unity. This result is…”
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Spectral moments of the real Ginibre ensemble by Byun, Sung-Soo, Forrester, Peter J.

“…The moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations,…”
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Asymptotic equidistribution and convexity for partition ranks by Males, Joshua

“…We study the partition rank function N ( r ,  t ;  n ), the number of partitions with rank congruent to r modulo t . We first show that it is monotonic in n…”
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On effective irrationality exponents of cubic irrationals by Badziahin, Dzmitry

“…We provide an upper bound for the effective irrationality exponents of cubic algebraics x with the minimal polynomial x 3 - t x 2 - a . In particular, we show…”
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On matching and periodicity for (N,α)-expansions by Kraaikamp, Cor, Langeveld, Niels

“…Recently a new class of continued fraction algorithms, the ( N , α )-expansions, was introduced in Kraaikamp and Langeveld (J Math Anal Appl 454(1):106–126,…”
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On the evaluation of the alternating multiple t value t(1¯,…,1¯,1,1¯,…,1¯) by Charlton, Steven

“…We prove an evaluation for the stuffle-regularised alternating multiple t value t ∗ , V ( 1 ¯ , … , 1 ¯ , 1 , 1 ¯ , … , 1 ¯ ) in terms of V , the…”
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Hypergeometric series, modular linear differential equations and vector-valued modular forms by Franc, Cameron, Mason, Geoffrey

“…We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the three-punctured…”
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On the total number of parts functions associated with ranks of partitions modulo 5 and 7 by Mao, Renrong

“…Recently, Andrews proved congruences for the total number of parts functions associated with ranks of partitions modulo 5 and 7. In this paper, applying the…”
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New proofs of some double sum Rogers–Ramanujan type identities by Wang, Liuquan

“…Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give…”
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On a variant of Pillai’s problem with factorials and S-units by Faye, Bernadette, Luca, Florian, Ziegler, Volker

“…Let S be a finite, fixed set of primes. In this paper, we show that the set of integers c which have at least two representations as a difference between a…”
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q-Analogues of two “divergent” Ramanujan-type supercongruences by Guo, Victor J. W.

“…Guillera and Zudilin proved three “divergent” Ramanujan-type supercongruences by means of the Wilf–Zeilberger algorithmic technique. In this paper we prove q…”
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On the Dotsenko–Fateev complex twin of the Selberg integral and its extensions by Neretin, Yury A.

“…The Selberg integral has a twin (‘the Dotsenko–Fateev integral’) of the following form. We replace real variables x k in the integrand ∏ | x k | σ - 1 | 1 - x…”
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On the exponential diophantine equation $$U_{n}^x+U_{n+1}^x=U_m by Batte, Herbert, Ddamulira, Mahadi, Kasozi, Juma, Luca, Florian

“…Abstract Let $$ \{U_n\}_{n\ge 0} $$ { U n } n ≥ 0 be the Lucas sequence. For integers x , n and m , we find all solutions to $$U_{n}^x+U_{n+1}^x=U_m$$ U n x +…”
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