Solomon Friedberg
Publication List

Theta functions, liftings, and generalized Hilbert modular forms, dissertation, The University of Chicago, June 1982.

On Maass wave forms and the imaginary quadratic Doi-Naganuma lifting, Mathematische Annalen 263 (1983), 483-508.

On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level, Nagoya Mathematical J. 92 (1983), 1-20.

Theta series correspondences and modular forms for number fields, in Modular Forms, Ellis Horwood, Ltd., 1984, 75-86.

Differential operators and theta series, Transactions A.M.S.287 (1985), 569-589.

Theta function transformation formulas and the Weil Representation, J. Number Theory 20 (1985), 121-127.

(with D. Bump, D. Goldfeld), Poincare series and Kloosterman sums, in The Selberg Trace Formula and Related Topics, Contemporary Mathematics, A.M.S., 1986, 39-49.

Lectures on Modular Forms and Theta Series Correspondences, Middle East Technical University Foundation, No. 1, Ankara, Turkey, 1986.

On theta functions associated to indefinite quadratic forms, J. Number Theory 23 (1986), 255-267.

Explicit determination of GL(n) Kloosterman sums, in Seminaire de Theorie des Nombres, Universite de Bordeaux I, 1985-1986, 22 pgs.

A global approach to the Rankin-Selberg convolution for GL(3,Z), Transactions A.M.S. 300 (1987), 159-174.

The Fourier expansion on a congruence subgroup of SL(n,Z) (appendix to a paper of D. Goldfeld), in Analytic Number Theory and Diophantine Problems, Birkhauser, 1987, 177-180.

Poincare series for GL(n) Fourier expansion, Kloosterman sums, and algebreo-geometric estimates, Mathematische Zeitschrift 196 (1987), 165-188.

Poincare series, Kloosterman sums, trace formulas, and automorphic forms for GL(n), in Seminaire de Theorie des Nombres, Paris, 1985-1986, Birkhauser, 1987, 53-66.

(with D. Bump, D. Goldfeld) Poincare series and Kloosterman sums for SL(3,Z), Acta Arithmetica 50 (1988), 31-89.

(with D. Bump) On Mellin transforms of unramified Whittaker functions on GL(3,C), J. Mathematical Analysis and Applications139 (1989), 205-216.

(with D. Bump, J. Hoffstein) A nonvanishing theorem for derivatives of automorphic L-functions with applications to elliptic curves, Bulletin A.M.S. 21 (1989), 89-93.

(with D. Bump) The exterior square automorphic L-functions on GL(n), in Festschrift in Honour of Prof. I.I. Piatetski-Shapiro, Israel Math. Conf. Proc. 3 (1990), 47-65.

(with D. Bump, J. Hoffstein) Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives, Annals of Mathematics 131 (1990), 53-127.

(with D. Bump, J. Hoffstein) Nonvanishing theorems for L-functions of modular forms and their derivatives, Inventiones Mathematicć 102 (1990), 543-618.

(with D. Bump, J. Hoffstein) The Kubota symbol for Sp(4,Q(i)), Nagoya Mathematical J. 119 (1990), 173-188.

(with D. Bump, J. Hoffstein) On Waldspurger's theorem, in Proceedings of the Conference on Automorphic Forms and Analytic Number Theory, Centre de Recherches Mathematiques, Montreal (1990), 25-36.

(with D. Bump, J. Hoffstein) Exterior algebra and the Iwasawa decomposition (appendix to a paper of E. Stade), Duke Mathematical J.60 (1990), 359-361.

(with S.-T. Wong) On the Shimura correspondence for GSp(4), Mathematische Annalen 290 (1991), 183-207.

(with D. Bump, J. Hoffstein) p-adic Whittaker functions on the metaplectic group, Duke Mathematical J. 63 (1991), 379-397.

(with D. Bump, D. Ginzburg) Whittaker-Orthogonal models, functoriality, and the Rankin-Selberg method, Inventiones Mathematicć 109 (1992), 55-96.

(with D. Goldfeld) Mellin transforms of Whittaker functions, Bulletin de la Societé Mathematique de France 121 (1993), 91-107.

(with H. Jacquet) Le lemme fondamental pour le sous-groupe de Shalika de GL(4), Comptes Rendus de l'Académie des Sciences, Paris 316, Serie I (1993), 407-410.

(with H. Jacquet) Linear periods, Journal für die Reine und Angewandte Mathematik 443 (1993), 91-139.

(with J. Hoffstein) Nonvanishing theorems for automorphic L-functions on GL(2), Annals of Mathematics 142 (1995), 385-423.

(with D. Bump, J. Hoffstein) On some applications of automorphic forms to number theory, Bulletin of the A.M.S. 33 (1996), 157--175.

(with H. Jacquet) The Fundamental Lemma for the Shalika Subgroup of GL(4), Memoirs of the A.M.S., Volume 124, No. 594, 1996.

(with D. Bump, M. Furusawa) Explicit formulas for the Waldspurger and Bessel models, Israel Journal of Mathematics, 102, 1997, 125-177.

(with D. Bump) Metaplectic generating functions and Shimura integrals, in Automorphic Forms, Automorphic Representations, and Arithmetic, Proc. Symp. Pure Math. 66, Part 2 (1999), 1--17.

(with D. Goldberg) On local coefficients for non-generic representations of some classical groups, Compositio Mathematicć (1999), 133--166.

(with D. Bump, D. Ginzburg) Rankin-Selberg integrals in two complex variables, Mathematische Annalen313 (1999), 731--761.

(with S. Gelbart, H. Jacquet, J. Rogawski) Représentations génériques du groupe unitaire ŕ 3 variables, Comptes Rendus de l'Académie des Sciences, Paris 329, Série I (1999), 255--260.

The Boston College Mathematics Case Studies Project, Mathematicians and Education Reform Forum 12 (2000), 10--12.

(with D. Bump, D. Ginzburg) A Rankin-Selberg integral using the automorphic minimal representation of SO(7), J. Ramanujan Math. Society 15 (2000), 81--124.

S. Friedberg and the BCCase Development Team, Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom, Issues in Mathematics Education Volume 10, American Mathematical Society, Providence RI, 2001. Faculty Edition ISBN 0-8218-2875-4; Graduate Student Edition ISBN 0-8218-2823-1.

(with D. Bump, D. Ginzburg) On the cubic Shimura lift for PGL3, Israel J. of Mathematics 126 (2001), 289--308.

A note on base change, identitites involving tau(n), and a congruence of Ramanujan, Ramanujan Journal 7, No. 1-3 (2003), 165-168 (Robert A. Rankin special memorial issues). 

(with D. Bump, D. Ginzburg) Small representations for odd orthogonal groups, International Mathematical Research Notices 2003:25 (2003), 1363--1393.

(with B. Fisher) Sums of twisted GL(2) L-functions over function fields, Duke Mathematical Journal 117 (2003), 543--570.

(with J. Hoffstein, D. Lieman) Double Dirichlet series and the n-th order twists of Hecke L-series, Mathematische Annalen 327 (2003), 315--338.

(with D. Bump, J. Hoffstein) Sums of twisted GL(3) automorphic L-functions, in Contributions to Automorphic Forms, Geometry and Arithmetic (H. Hida, D. Ramakrishnan and F. Shahidi, eds.), Johns Hopkins Univ. Press, 2004, pp. 131--162.

(with B. Fisher) Double Dirichlet series over function fields, Compositio Mathematica 140 (2004), 613--630.

Teaching mathematics graduate students how to teach, Notices of the American Mathematical Society 52 (2005), 842--847.

(with B. Brubaker, J. Hoffstein)  Cubic twists of GL(2) automorphic L-functions,  Inventiones Math. 160 (2005), 31--58.

(with G. Chinta, J. Hoffstein) Asymptotics for sums of twisted L-functions and applications, in: Automorphic Representations, L-functions and Applications: Progress and Prospects,  Ohio State University Mathematical Research Institute Publications 11, de Gruyter, 2005, pp. 75--94.

(with B. Brubaker, D. Bump, J. Hoffstein)  Gelfand-Tsetlin interpretation of Chinta's A_5 polynomial, 1,012 page manuscript (too long to be formally published).

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory, edited by S. Friedberg (Managing Editor), D. Bump, D. Goldfeld, J. Hoffstein, Proceedings of Symposia in Pure Mathematics, Volume 75, American Mathematical Society (Providence, RI), 2006.

(with G. Chinta, J. Hoffstein) Multiple Dirichlet series and automorphic forms, Proc. Symp. Pure Math. 75 (2006), 3--41.

(with B. Brubaker, D. Bump, G. Chinta, J. Hoffstein) Weyl group multiple Dirichlet series I, Proc. Symp. Pure Math. 75 (2006), 91--114.

(with D. Bump, D. Ginzburg)  Lifting automorphic representations on the double covers of orthogonal groups,  Duke Mathematical Journal 131 (2006), 363--396.

(with B. Brubaker, D. Bump) Weyl group multiple Dirichlet series II:  the stable case, Inventiones Math 165 (2006), 325--355.

Teaching mathematics graduate students to teach:  an international perspective, in: Enhancing University Mathematics, Proceedings of the First KAIST International Symposium on Teaching (Ko and Arganbright, eds.),  Issues in Mathematics Education Vol. 14, American Mathematical Society, Providence RI, 2007, pp. 51--55. 
A previous version of these proceedings was circulated as a bound volume Proceedings of the First KAIST International Symposium on Enhancing University Mathematics Teaching,  Korean Advanced Institute of Science and Technology, Daejeon, Korea, 2005, and an earlier version of this article is on pages 177--181 of that volume. 

(with A. Ash) Hecke L-functions and the distribution of totally positive integers, Canadian Journal of Mathematics 59 (2007), 673--695.

(with B. Brubaker, D. Bump, J. Hoffstein) Weyl group multiple Dirichlet series III: Eisenstein series and twisted unstable A_r, Annals of Math. 166 (2007), 293--316.

(with B. Brubaker, D. Bump) Twisted Weyl group multiple Dirichlet series:  the stable case, in: Eisenstein Series and Applications (Gan, Kudla and Tschinkel, eds.), Progress in Math Vol. 258, Birkhäuser, 2008, pp. 1--26.

(with G. Chinta, P. E. Gunnells) On the p-parts of quadratic Weyl group multiple Dirichlet series, to appear in Journal für die Reine und Angewandte Mathematik  623 (2008), 1--23.

(with B. Brubaker, D. Bump) Gauss sum combinatorics and metaplectic Eisenstein series, in:  Automorphic Forms and L-functions I: Global Aspects (Ginzburg, Lapid and Soudry, eds.), Contemporary Mathematics Vol. 488, American Mathematical Society, 2009, pp. 61--81. 

Euler products and twisted Euler products,  in: Automorphic forms and the Langlands Program (Ji, Liu, Yau and Zheng, eds.), Advanced Lectures in Mathematics, Vol. 9,  International Press, 2010, pp. 176--198.  Published jointly by International Press and by Higher Education Press of China.

(with B. Brubaker, D. Bump) Weyl Group Multiple Dirichlet Series:  Type A Combinatorial Theory,  Annals of Mathematics Studies, Volume 175, Princeton University Press, 2011.

(with B. Brubaker, D. Bump) Weyl group multiple Dirichlet series, Eisenstein series and crystal bases, Annals of Mathematics 173 (2011), 1081-1120.

(with B. Brubaker, D. Bump) Schur polynomials and the Yang-Baxter equation, Communications in Mathematical Physics 308 (2011), 281-301.

(with B. Brubaker, D. Bump) Eisenstein series, crystals and ice,  Notices of the American Mathematical Society 58 (2011), 1563-1571.

Teaching teachers:  roles for mathematicians (Preparando profesores: el papel de los matemáticos),  Pensamiento Educativo, Revista de Investigación Educacional Latinoamericana 49(1), 2012, 32-39.

(with B. Brubaker, D. Bump and J. Hoffstein) Coefficients of the n-fold theta function and Weyl group multiple Dirichlet series, in:  Contributions in Analytic and Algebraic Number Theory (Blomer, Mihăilescu, eds.), Springer Proceedings in Math., Vol. 9, Springer, 2012, pp. 83-95.

(with G. Chinta, J. Hoffstein) Double Dirichlet series and theta functions, in:  Contributions in Analytic and Algebraic Number Theory (Blomer, Mihăilescu, eds.), Springer Proceedings in Math., Vol. 9, Springer, 2012, pp.149-170.

(with B. Brubaker, D. Bump, G. Chinta and P. E. Gunnells) Metaplectic ice, in: Multiple Dirichlet Series, L-Functions and Automorphic Forms (Bump, Friedberg, Goldfeld, eds.), Progress in Mathematics, Vol. 300, Birkhäuser Boston, 2012, pp. 65-92.

Multiple Dirichlet Series, L-Functions and Automorphic Forms, edited by D. Bump, S. Friedberg and D. Goldfeld, Progress in Mathematics, Vol. 300, Birkhäuser Boston, 2012.

(with B. Brubaker, D. Bump) Unique functionals and representations of Hecke algebras, Pacific Journal of Mathematics 260(2) (2012), 381-394. (This is the issue in memory of Jonathan Rogawski.) DOI 10.2140/pjm.2012.260.381.

(with D. Ginzburg) Metaplectic theta functions and global integrals, Journal of Number Theory 146 (2015),  134-149 (special issue in memory of Steve Rallis). DOI: 10.1016/j.jnt.2014.04.001.

(with L. Zhang) Eisenstein series on covers of odd orthogonal groups, American Journal of Mathematics 137 (2015), 953-1011.   DOI: 10.1353/ajm.2015.003. 

(with B. Brubaker) Whittaker coefficients of metaplectic Eisenstein series, Geometric and Functional Analysis (GAFA) 25(4) (2015), 1180-1239.  DOI: 10.1007/s00039-015-0329-4.

(with B. Brubaker, D. Bump) Matrix coefficients and Iwahori-Hecke algebra modules, Advances in Mathematics 299 (2016), 247-271.  DOI: 10.1016/j.aim.2016.05.012.

(with D. Ginzburg) Criteria for the existence of cuspidal theta representations, Research in Number Theory 2(1) (2016), 1-16.  DOI 10.1007/s40993-016-0046-6.

(with L. Zhang) Tokuyama-type formulas for type B, Israel Journal of Mathematics 216(2) (2016), 617-655.  DOI: 10.1007/s11856-016-1422-6.

(with D. Ginzburg) On the genericity of Eisenstein series and their residues for covers of GLm, International Mathematics Research Notices (IMRN) 2017(4) (2017), 1000-1012. DOI: 10.1093/imrn/rnw042.

The contributions of mathematics faculty to K-12 education: a department chair’s perspective, to appear in Mathematics Matters in Education - Essays in Honor of Roger E. Howe (Li, Lewis, Madden, eds.), Springer.

(with D. Ginzburg) Descent and theta functions for metaplectic groups, to appear in the Journal of the European Mathematical Society (JEMS).

(with D. Ginzburg) Theta functions on covers of symplectic groups, to appear in Automorphic Forms, L-functions and Number Theory, a special issue of BIMS in honor of Prof. Freydoon Shahidi's 70th birthday.

(with Y. Cai, D. Ginzburg, and E. Kaplan) Doubling constructions for covering groups and tensor product L-functions, preprint (66 pgs). Research announcement:  arXiv:1601.08240.

(with B. Brubaker, V. Buciumas, and D. Bump) Hecke modules from metaplectic ice, preprint.

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Last update:   April 4, 2017