## Analytic number theory, modular forms and $$q$$-hypergeometric series. In honor of Krishna Alladi’s 60th birthday, University of Florida, Gainesville, FL, USA, March 17–21, 2016.(English)Zbl 1388.11003

Springer Proceedings in Mathematics & Statistics 221. Cham: Springer (ISBN 978-3-319-68375-1/hbk; 978-3-319-68376-8/ebook). l, 736 p. (2017).
Publisher’s description: Gathered from the 2016 Gainesville number theory conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi’s own research on partitions and $$q$$-series as well as his earlier work in number theory.
Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and $$q$$-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
The articles of this volume will be reviewed individually.
Indexed articles:
Adhikari, Sukumar Das, Plus-minus weighted zero-sum constants: a survey, 1-9 [Zbl 1391.11022]
Andersen, Nickolas, Vector-valued modular forms and the seventh order mock theta functions, 11-23 [Zbl 1433.11047]
Andrews, George E., The Alladi-Schur polynomials and their factorization, 25-38 [Zbl 1416.11152]
Banerjee, Koustav; Dixit, Atul, New representations for $$\sigma (q)$$ via reciprocity theorems, 39-57 [Zbl 1390.33030]
Benli, Kübra; Elma, Ertan; Yıldırım, Cem Yalçın, Mean values of the functional equation factors at the zeros of derivatives of the Riemann zeta function and Dirichlet $$L$$-functions, 59-67 [Zbl 1432.11114]
Berkovich, Alexander; Uncu, Ali Kemal, New weighted partition theorems with the emphasis on the smallest part of partitions, 69-94 [Zbl 1393.05042]
Berndt, Bruce C., The appearance of H. F. Baker and E. W. Hobson in “The man who knew infinity”, 95-97 [Zbl 1390.01070]
Bhatnagar, Gaurav, A bibasic Heine transformation formula and Ramanujan’s $$_2\phi_1$$ transformations, 99-122 [Zbl 1390.33031]
Borwein, Jonathan M., Adventures with the OEIS, 123-138 [Zbl 1390.11055]
Bringmann, Kathrin; Mahlburg, Karl, Three-colored partitions and dilated companions of Capparelli’s identities, 139-156 [Zbl 1390.05018]
Chen, William Y. C.; Ji, Kathy Q.; Zang, Wenston J. T., Nearly equal distributions of the rank and the crank of partitions, 157-177 [Zbl 1416.11144]
Cooper, Shaun; Wan, James G.; Zudilin, Wadim, Holonomic alchemy and series for $$1/\pi$$, 179-205 [Zbl 1391.11165]
Deshouillers, Jean-Marc; Grekos, Georges, Integral points on a very flat convex curve, 207-212 [Zbl 1433.11082]
Dousse, Jehanne, Unification, refinements and companions of generalisations of Schur’s theorem, 213-251 [Zbl 1416.11145]
Ekhad, Shalosh B.; Zeilberger, Doron, Integrals involving Rudin-Shapiro polynomials and sketch of a proof of Saffari’s conjecture, 253-265 [Zbl 1391.11050]
Elliott, P. D. T. A., From Ramanujan to groups of rationals: a personal history of abstract multiplicative functions, 267-295 [Zbl 1426.11101]
Goldfeld, Dorian, On an additive prime divisor function of Alladi and Erdős, 297-309 [Zbl 1426.11102]
Hirschhorn, Michael D., Ramanujan’s tau function, 311-328 [Zbl 1433.11040]
Jha, Abhash Kumar; Kumar, Arvind, Construction of cusp forms using Rankin-Cohen brackets, 329-341 [Zbl 1433.11048]
Kanade, Shashank; Kurşungöz, Kağan; Russell, Matthew, An open problem of Corteel, Lovejoy, and Mallet, 343-370 [Zbl 1416.11157]
Kimport, Susie, On the asymptotics of partial theta functions, 371-392 [Zbl 1433.11046]
Kolitsch, Louis W., Overpartitions and truncated partition identities, 393-400 [Zbl 1416.11147]
Krattenthaler, Christian, Congruences modulo powers of 2 for the number of unique path partitions, 401-408 [Zbl 1390.05012]
Kryuchkov, Sergey I.; Lanfear, Nathan A.; Suslov, Sergei K., Complex form of classical and quantum electrodynamics, 409-443 [Zbl 1393.35232]
Liu, Zhi-Guo, On a system of $$q$$-partial differential equations with applications to $$q$$-series, 445-461 [Zbl 1401.05046]
Lovejoy, Jeremy, Asymmetric generalizations of Schur’s theorem, 463-476 [Zbl 1416.11148]
Luca, Florian; Pomerance, Carl, Local behavior of the composition of the aliquot and co-totient functions, 477-495 [Zbl 1421.11076]
McIntosh, Richard J., On the universal mock theta function $$g_2$$ and Zwegers’ $$\mu$$-function, 497-502 [Zbl 1433.11050]
Mc Laughlin, James, Mock theta function identities deriving from bilateral basic hypergeometric series, 503-531 [Zbl 1391.33034]
Montgomery, Hugh L., Littlewood polynomials, 533-553 [Zbl 1391.42004]
Nathanson, Melvyn B., Trapezoidal numbers, divisor functions, and a partition theorem of Sylvester, 555-586 [Zbl 1393.05046]
Nicolas, Jean-Louis, Estimates of $$\mathrm{li}(\theta (x))-\pi (x)$$ and the Riemann hypothesis, 587-610 [Zbl 1426.11109]
Ono, Ken; Schneider, Robert; Wagner, Ian, Partition-theoretic formulas for arithmetic densities, 611-624 [Zbl 1416.11151]
Paule, Peter; Radu, Cristian-Silviu, A new witness identity for $$11\mid p(11n+6)$$, 625-639 [Zbl 1416.11155]
Ramakrishnan, B.; Sahu, Brundaban; Singh, Anup Kumar, On the representations of a positive integer by certain classes of quadratic forms in eight variables, 641-664 [Zbl 1426.11026]
Saradha, N.; Sharma, Divyum, A note on Thue inequalities with few coefficients, 665-675 [Zbl 1390.11076]
Schlosser, Michael J.; Yoo, Meesue, Basic hypergeometric summations from rook theory, 677-692 [Zbl 1391.33035]
Seo, Seunghyun; Yee, Ae Ja, Overpartitions and singular overpartitions, 693-711 [Zbl 1391.05043]
Sills, Andrew V., A classical $$q$$-hypergeometric approach to the $$A_2^{(2)}$$ standard modules, 713-731 [Zbl 1391.33036]
Tenenbaum, Gérald, Generalized Mertens sums, 733-736 [Zbl 1426.11098]

### MSC:

 11-06 Proceedings, conferences, collections, etc. pertaining to number theory 11B65 Binomial coefficients; factorials; $$q$$-identities 11F30 Fourier coefficients of automorphic forms 11K65 Arithmetic functions in probabilistic number theory 11N05 Distribution of primes 11P84 Partition identities; identities of Rogers-Ramanujan type 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$ 00B30 Festschriften 00B25 Proceedings of conferences of miscellaneous specific interest